All Seminars [Hide Abstracts]
Fall 2010

Colloquium
 Reaction-diffusion system with skew-gradient structure Link: View Poster Speaker: Chao Nien Chen (National Changhua University of Education, Taiwan.) Faculty Sponsor:Choi Time: Monday, July 26, 2010 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Reaction-diffusion systems with skew-gradient structure can be viewed as a sort of activator-inhibitor systems. A well-known example is FitzHugh Nagumo system. In conjunction with calculus of variations, there is a close relation between the stability of a steady state and its relative Morse index. We discuss how to use variational methods to study the existence and stability of steady states of such systems.

S.I.G.M.A. Seminar
 Infinitesimals and Nonstandard Calculus Link: View Poster Speaker: Reed Solomon (University of Connecticut) Time: Friday, September 3, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: To define the real numbers from the rational numbers, we "fill in the gaps" in the rational numbers using Cauchy sequences or some similar process. In nonstandard analysis, we go one step further by adding infinitesimals elements to the reals. (You can think of this process as "filling in the gaps" in the reals!) In this Sigma talk, I will explain how to construct such an extension of the reals and how such an extension can be used to prove theorems of calculus without ever mentioning a limit. Comments: Free Pizza (courtesy of Mathematics Department)

 Cluster algebras from surfaces Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Wednesday, September 8, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 The Symmetric Function Theorem Link: View Poster Speaker: Keith Conrad (University of Connecticut) Time: Wednesday, September 8, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Polynomials like x4 + y4, which don't change when we  exchange the variables (replacing x with y and y with x),  are called symmetric.   The simplest symmetric polynomials come from addition and multiplication:  x + y and xy.    The fundamental theorem of symmetric polynomials in two variables says that every symmetric polynomial in x and y is a polynomial in the basic symmetric polynomials x + y and xy.  For example,  x4 + y4 = (x+y)4 - 4(x+y)2(xy) + 2(xy)2.  We will prove a version of this fundamental theorem for symmetric polynomials in any number of variables (not just two variables) and describe some applications to questions about polynomials in one variable. For example, you can determine if a quadratic polynomial ax2 + bx + c has a repeated root by checking if b2 - 4ac = 0 (think about the quadratic formula). We will use symmetric polynomials to see how this kind of rule generalizes to polynomials of higher degree. Comments: Free Refreshments -- uconnmathclub@gmail.com --

S.I.G.M.A. Seminar

Logic Seminar
 Existentially closed dimension groups Link: View Poster Speaker: Philip Scowcroft (Wesleyan University) Time: Monday, September 13, 2010 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: A dimension group is a special kind of partially ordered Abelian group first studied in connection with operator algebras. Existentially closed dimension groups are to dimension groups as algebraically closed fields are to fields. This talk will explain all the terms in its title and characterize the existentially closed dimension groups.

Actuarial Science Seminar
 Title TBD Link: View Poster Speaker: Jim Bridgeman (University of Connecticut) Time: Tuesday, September 14, 2010 at 1:00 pm Place: MSB 215 (UConn - Storrs)

Algebra Seminar
 Cluster variables of cluster algebras Link: View Poster Speaker: Kyungyong Lee (University of Connecticut) Time: Tuesday, September 14, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Fomin and Zelevinsky introduced cluster algebras and proved the Laurent phenomenon of cluster variables. In addition, they conjectured that the coefficients of monomials in the Laurent expression of cluster variables are non-negative integers. This conjecture implies positivity of the Euler characteristics of certain quiver Grassmannians. After reviewing some of the main results on cluster algebras, we present a natural approach to the positivity conjecture.

 Cluster algebras from surfaces II Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Wednesday, September 15, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 Diophantine Approximation for the Masses Link: View Poster Speaker: Avi Bourla (University of Connecticut) Time: Wednesday, September 15, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Named after the "father of algebra", Diophantus of Alexandria circa 200AD, Diophantine approximation is a field in number theory concerned with the approximation of real numbers using rational numbers. Whereas any real number can be approximated using rationals to any degree of accuracy, Diophantine Approximation concerns those rationals which are of the best quality, that is, those that combine accuracy with simplicity. For instance, the approximation errors for 314159/100000 = 3.14159 and 355/113=3.1415920353982 to π are very close, yet the latter fraction has a much smaller denominator, making it of better quality than the former. In this talk, we'll discuss about the beautifully simple theory behind finding these good quality approximations. Comments: Free Refreshments -- Email: uconnmathclub@gmail.com -- "Like" the UConn Math Club page on Facebook!

Colloquium
 Folding Carpenter's Rules, Robot Arms, Proteins: from geometry to combinatorics Link: View Poster Speaker: Ileana Streinu (Smith College) Faculty Sponsor:Hering Time: Thursday, September 16, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The Carpenter's Rule problem, first appearing in the topology community in the mid '70s and then in Computer Science in the '90's as a robot arm motion planning problem, asks whether every simple planar polygon with fixed edge lengths can be reconfigured continuously between two positions, without producing any self-intersections along the way. The solution is a mixture of ideas from geometry, rigidity theory and polyhedral combinatorics, all leading to a curious (but nice and friendly) object, called a pseudo-triangulation. A main attraction of this talk is its graphical appeal: every concept I define is elementary, depicted graphically (with lots of two- and three-dimensional props) and easy to understand. The "protein" part of the title leads to the future, to one of the major problems in science today (protein folding): I will conclude telling you what is the connection between folding a robot arm and a protein, and where is this research leading to.

S.I.G.M.A. Seminar
 Nuts and Bolts of the Black-Scholes PDE Solution Link: View Poster Speaker: Edward Perry (University of Connecticut) Time: Friday, September 17, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We will discuss the meaning of the price of a financial derivative in general, and an option price in particular. In the financial world, the Black-Scholes equation is used to price options; we will present the “Nuts and Bolts” of working through the Black-Scholes Partial Differential Equation. Starting with the PDE and effecting a number of substitutions, we transform it into the Heat Equation, which has a convivial solution. The PDE result is compared against a probabilistic solution and found to be the same. Comments: Free Pizza (courtesy of Mathematics Department)

Logic Seminar
 Finitely generic dimension groups Link: View Poster Speaker: Philip Scowcroft (Wesleyan University) Time: Monday, September 20, 2010 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: Finitely generic dimension groups form a subclass of the existentially closed dimension groups. After outlining the method of model-theoretic forcing used to produce finitely generic dimension groups, this talk will describe algebraic and recursion-theoretic properties distinguishing these groups from arbitrary existentially closed dimension groups.

Algebra Seminar
 Cluster variables of cluster algebras (Part 2) Link: View Poster Speaker: Kyungyong Lee (University of Connecticut) Time: Tuesday, September 21, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Fomin and Zelevinsky introduced cluster algebras and proved the Laurent phenomenon of cluster variables. In addition, they conjectured that the coefficients of monomials in the Laurent expression of cluster variables are non-negative integers. This conjecture implies positivity of the Euler characteristics of certain quiver Grassmannians. After reviewing some of the main results on cluster algebras, we present a natural approach to the positivity conjecture.

 Cluster expansion formula Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Wednesday, September 22, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

 Introduction and Overview Link: View Poster Speaker: Ryan Kinser (University of Connecticut) Time: Wednesday, September 22, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 Subspace Arrangements Link: View Poster Speaker: Ryan Kinser (University of Connecticut) Time: Wednesday, September 22, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: A subspace arrangement is a configuration of subspaces in a vector space. For example, it could be a configuration of lines in a plane, or both lines and planes in 3-d space. Two subspace arrangements can be considered the "same" if you can get from one to the other just by changing coordinates in your space. We will also discuss some combinatorial aspects of subspace arrangements, and when there are finitely many vs. infinitely many subspace arrangements with given dimensions. Comments: Free Refreshments -- Email: uconnmathclub@gmail.com -- "Like" the UConn Math Club page on Facebook!

Colloquium
 Memorization or understanding: are we teaching the right thing? Link: View Poster Speaker: Eric Mazur (Harvard University) Time: Thursday, September 23, 2010 at 4:30 pm Place: BPB 131 (UConn - Storrs) Abstract: Education is more than just transfer of information, yet that is what is mostly done in large introductory courses -- instructors present material (even though this material might be readily available in printed form) and for students the main purpose of lectures is to take down as many notes as they can. Few students have the ability, motivation, and discipline to synthesize all the information delivered to them. Yet synthesis is perhaps the most important -- and most elusive -- aspect of education. I will show how shifting the focus in lectures from delivering information to synthesizing information greatly improves the learning that takes place in the classroom Comments: Note unusual time and place!

Mathematics Education
 Memorization or understanding: are we teaching the right thing? Link: View Poster Speaker: Eric Mazur (Harvard University) Faculty Sponsor:Cardetti Time: Thursday, September 23, 2010 at 4:30 pm Place: Biology Physics Building BPB 131 (UConn - Storrs) Abstract: Education is more than just transfer of information, yet that is what is mostly done in large introductory courses -- instructors present material (even though this material might be readily available in printed form) and for students the main purpose of lectures is to take down as many notes as they can. Few students have the ability, motivation, and discipline to synthesize all the information delivered to them. Yet synthesis is perhaps the most important -- and most elusive -- aspect of education. I will show how shifting the focus in lectures from delivering information to synthesizing information greatly improves the learning that takes place in the classroom

PDE and Differential Geometry Seminar
 Convexity of level sets of solutions to nonlinear PDEs Link: View Poster Speaker: Pengfei Guan (McGill University) Time: Monday, September 27, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Solutions of partial differential equations of boundary value problems inherit certain geometric properties of the domains and the structural of the corresponding equations. We will discuss a recent joint work with Lu Xu on the level set convexity problem for solutions of general nonlinear PDE $F(D^2u, Du, u, x)=0$. We explain how can we obtain geometric estimates for the principal curvatures of the level sets under proper structural conditions on $F$.

Logic Seminar
 Computable Structure Theory of Uncountable (Size Aleph_1) Linear Orders Link: View Poster Speaker: Asher Kach (University of Connecticut) Time: Monday, September 27, 2010 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: In this talk, we will begin by introducing a framework (alpha-recursion theory over the ordinal omega_1) for the development of computability theory and computable structure theory over the domain omega_1. We will also quickly review certain classical linear orders. Then, within this framework, we analyze the computable structure theory of linear orders of size (at most) aleph_1. In particular, we characterize the omega_1-computably categorical linear orders and discuss the degree spectra of the successor relation.

Algebra Seminar
 Autoequivalences and stability conditions Link: View Poster Speaker: Parker Lowrey (University of Western Ontario) Time: Tuesday, September 28, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: I will discuss how stability conditions and well adapted autoequivalences can be used to understand geometric information in derived categories. Following this discussion, I will provide an example of the usefulness of these techniques. In particular, I will show how to classify all compactifications of stable bundles on a class of genus 0 singular reducible curves.

 F-polynomials and g-vectors Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Wednesday, September 29, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

 Introduction and Overview, Part 2 Link: View Poster Speaker: Ryan Kinser (University of Connecticut) Time: Wednesday, September 29, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 Fourier Series and the Isoperimetric Inequality Link: View Poster Speaker: John Haga (University of Connecticut) Time: Wednesday, September 29, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Most Mathematics students are familiar with the concept of "inner product" as it pertains to R^n (i.e. taking the dot product of two vectors in Euclidean space). There are other spaces where the inner product is defined; in particular in L²(S_1), the vector space of square integrable functions on the circle. We will see that the functions sin(nx)/π and cos(mx)/π form an orthonormal basis for this vector space and that projection of a function f onto this basis is tantamount to finding the Fourier series representation of f. Fourier series are extremely useful in Mathematics, Physics and Engineering. We will see how we can use Fourier series to prove the classical isoperimetric inequality: of all regions in the plane with fixed area A, the region with the shortest boundary is the circle of area A. Comments: Free Refreshments -- Email: uconnmathclub@gmail.com -- "Like" the UConn Math Club page on Facebook!

S.I.G.M.A. Seminar
 Error-Correcting Codes: Toric Construction Link: View Poster Speaker: Ryan Schwarz (University of Connecticut) Time: Friday, October 1, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Since toric codes were introduced by J. Hansen in 1998, they have become a topic of interest due to their connections with combinatorics, algebraic geometry, and of course coding theory. From the coding theory perspective, this code construction has led to the discovery of codes with exceptional error-correction capability. This talk will explain the basics of what a code is and how codes can correct errors picked up through transmission. Then we will discuss the construction of toric codes, giving some examples with good error control, and if time permits, give a classification of toric codes of small dimension. Comments: Free Pizza (courtesy of Mathematics Department)

PDE and Differential Geometry Seminar
 On Hamilton's Ricci Flow and Bartnik's Construction of Metrics of Prescribed Scalar Curvature Link: View Poster Speaker: Chen-Yun Lin (University of Connecticut) Time: Monday, October 4, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: It is known by work of R. Hamilton and B. Chow that the evolution under Ricci flow of an arbitrary initial metric $g$ on $S^2$, suitably normalized, exists for all time and converges to a round metric. In this talk, we will describe a construction for metrics of prescribed scalar curvature using solutions to the Ricci flow. The problem is converted into a semilinear parabolic equation similar to the quasispherical construction of Bartnik. We obtain existence results for this equation and applications of such metrics.

Algebra Seminar
 Quantum affine algebras, canonical bases and q-deformation of arithmetical functions Link: View Poster Speaker: Kyu-Hwan Lee (University of Connecticut) Time: Tuesday, October 5, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk, we consider affine analogues of Gindikin-Karpelevich formula and Casselman-Shalika formula as sums over Kashiwara-Lusztig’s canonical bases. Suggested by these formulas, we define natural q-deformation of arithmetical functions such as the multi-partition function and the Ramanujan tau-function, and prove various identities among them. In some examples, we recover classical identities by taking limits. We also consider the q-deformation of Kostant's function and study certain q-polynomials whose special values are weight multiplicities. This is a joint work with Henry Kim.

UConn Math Club
 Geometry and the Complexity of Computation Link: View Poster Speaker: Jessica Sidman (Mount Holyoke College) Time: Wednesday, October 6, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: We'll learn how to think about a curve in 3-space algebraically. This will lead us to some fundamental questions about polynomials. For example, suppose that f and g are polynomials in n variables. How can we determine if a given polynomial h can be written in the form h=af+bg, where a and b are also polynomials of n variables? By the end we'll see why a theorem on polynomials in 4 variables is best interpreted in terms of curves, and open problems will be posed. Comments: Free Refreshments -- Email: uconnmathclub@gmail.com -- "Like" the UConn Math Club page on Facebook!

Colloquium
 Representation theory of hyperplane arrangements Link: View Poster Speaker: Tom Braden (University of Massachusetts at Amherst) Faculty Sponsor:Hering Time: Thursday, October 7, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: To an arrangement of n hyperplanes in a rational vector space we associate an algebra of polynomial differential operators on affine n-space. The structure of modules over this algebra has many parallels with the classical representation theory of Lie algebras and their enveloping algebras. The underlying connection is geometric: both kinds of algebras can be obtained by quantizing the ring of functions on a symplectic manifold. For most of the talk, however, I will explore the parallels via elementary, down-to-earth examples. This is joint work with Anthony Licata, Nicholas Proudfoot and Ben Webster.

S.I.G.M.A. Seminar
 Partition functions and their q-deformations Link: View Poster Speaker: Kyu-Hwan Lee (University of Connecticut) Time: Friday, October 8, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: After we introduce multi-partition functions and the identities they satisfy, we will consider their q-deformations. Then I will explain the algebraic structures behind these q-deformations, that is, the quantum affine algebras. Comments: Free Pizza (courtesy of Mathematics Department)

PDE and Differential Geometry Seminar
 Ground states for the nonlinear Schroedinger-equation with interface Link: View Poster Speaker: Wolfgang Reichel (Karlsruhe Institute of Technology) Time: Monday, October 11, 2010 at 3:15 pm Place: MSB 118 (UConn - Storrs) Abstract: We are interested in ground states for the nonlinear Schrödinger-equation (NLS) with an interface between two purely periodic media. This means that the coefficients in the NLS model two different periodic media in each halfspace. The resulting problem no longer has a periodic structure. Using variational methods we give conditions on the coefficients such that ground states are created/prevented by the interface.

Logic Seminar
 Geometric model theory in efficient computability Link: View Poster Speaker: Cameron Hill (University of Notre Dame) Time: Monday, October 11, 2010 at 4:05 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: This talk will consist of a sketch of the proof of a single main result linking geometric ideas from the first-order model theory of infinite structures with complexity-theoretic analyses of problems over classes of finite structures. To remove any suspense, the statement of the theorem is as follows: Theorem: Let K = fin[T^G], where T is a complete k-variable theory with infinitely many finite models up to isomorphism. I. If T is constructible, then K is rosy. II. T is efficiently constructible if and only if K is super-rosy. Obviously, a great number of definitions are needed (regardless of the reader's background, most likely) to make sense of these assertions. For the time being, it should be understood as a shadow of the main current'' of first-order model theory -- namely, Shelah's Classification theory. I take efficiently constructible'' -- meaning that models of T can be efficiently recovered from elementary diagrams of subsets -- to be a reasonable substitute for classifiable'' in the classical theory. We then seek a hierarchy of structural properties culminating in efficient constructibility in analogy with the stability-theoretic hierarchy, Stable properly contains Super-stable properly contains Classifiable=Super-stable+NDOP. In the classical scenario, any non-trivial bound on the number of models of the theory in each cardinality imposes stability, which already supports the rudimentary notion of geometry known as non-forking independence. In the scenario of this study, the hypothesis of constructibility by an algorithm cursorily imitating that of an efficient algorithm in form (meaning, an essentially inflationary program which isn't necessarily efficient) is sufficient to impose another rudimentary notion of geometry on the class of models -- in this case, known as thorn-independence in a rosy class; this is the content of I of the Theorem. The further requirement of efficiency -- polynomially-bounded running times -- induces a further guarantee of good behavior in the geometry of thorn-independence, and the "only if" portion of II of the theorem amounts to just this fact. It turns out, then, that this additional tractability in the geometry gives enough purchase to devise an efficient algorithm, initially disguised as a weak model-theoretic coordinatization result, for the class of the theory's finite models.

Logic Seminar
 Computable Fields and the Bounded Turing Reduction Link: View Poster Speaker: Rebecca Steiner (CUNY) Time: Monday, October 11, 2010 at 5:05 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: For a computable field F, the splitting set S_F of F is the set of polynomials with coefficients in F which factor over F, and the root set R_F of F is the set of polynomials with coefficients in F which have a root in F. Results of Frohlich and Shepherdson from 1956 imply that for a computable field F, the splitting set S_F and the root set R_F are Turing-equivalent. Much more recently, R. G. Miller showed that for algebraic fields, the root set actually has slightly higher complexity: for algebraic fields F, it is always the case that S_F 1-reduces to R_F, but there are algebraic fields F where we have R_F not 1-reducible to S_F. Here we compare the splitting set and the root set of a computable algebraic field under a different reduction: the bounded Turing reduction. We construct a computable algebraic field for which R_F does not bT-reduce to S_F. We also define a Rabin embedding g of a field into its algebraic closure, and for a computable algebraic field F, we compare the relative complexities of R_F, S_F, and g(F) under m-reducibility and under bT-reducibility.

Algebra Seminar
 Polynomial families of tautological classes on the moduli space of curves Link: View Poster Speaker: Renzo Cavallieri (Colorado State University) Time: Tuesday, October 12, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The moduli space of curves is a key object in algebraic geometry. Its points correspond to either complex structures on a topological orientable surface of a fixed genus g, or to smooth projective algebraic curves of genus g. This space is then suitably compactified, and we are interested in studying intersection theory on this space. Since this is an overly ambitious goal, we restrict our attention to tautological intersection theory, concerned with classes that can be constructed "naturally" from the geometry of families of curves. There is a standard set of tautological classes that are used to generate the tautological intersection ring. Then there are classes that we know to be tautological, but that are very difficult to express in terms of standard generators. For certain families of such classes we present an algorithm to attain this task. This is joint work with Steffen Marcus (Brown U.)

Actuarial Science Seminar
 Leveraging Your Math Skills by Adding People Dynamics and Awareness Link: View Poster Speaker: Clifford Lange (Boston Mutual) Time: Tuesday, October 12, 2010 at 4:30 pm Place: MSB 411 (UConn - Storrs) Abstract: Do you have strong technical skills? How would you like to leverage the impact of combining these skills with strong people skills too? Did you know that 25% of people think they are in the top 1% with people skills? Come listen and learn more about how you can enhance your marketability and relationships through people skills. Find out more about how to do this and to hear some revealing examples of what was learned “the hard way”, so you don’t have to learn it “the hard way”.

 Strings and cluster variables Link: View Poster Speaker: Ilke Canakci (University of Connecticut) Time: Wednesday, October 13, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

 Quantum affine algebras Link: View Poster Speaker: Kyu-Hwan Lee (University of Connecticut) Time: Wednesday, October 13, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 The Basics of Fractal Geometry Link: View Poster Speaker: Dan Kelleher (University of Connecticut) Time: Wednesday, October 13, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Starting in the second half of the 19th century, mathematicians began to notice objects that baffled contemporary calculus and analysis, e.g. von Koch's continuous but nowhere differentiable curve or Cantor's uncountable, nowhere dense, perfect "middle thirds" set. Benoit Mandelbrot coined the term fractal to deal with these increasingly common and relevant objects. We shall talk about the basic concepts which are used to understand the bizarre geometry of such sets. Comments: Free Refreshments -- uconnmathclub@gmail.com -- "Like" the UConn Math Club on Facebook!

Colloquium
 The Polynomial Hirsch Conjecture and Polymath3 Link: View Poster Speaker: Gil Kalai (Hebrew University of Jerusalem/Yale) Faculty Sponsor:Ron Blei Time: Thursday, October 14, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: A) Hirsch's conjecture asserting that the graph of every d-polytope with n facets has diameter at most n-d was recently dosproved by Francisco Santos. But is there an upper bound (instead n-d) which is polynomial in n and d? B) Here is a related simple combinatorial problem: Consider t disjoint families of subsets of {1,2,…,n}, F_1, F_2, ... ,F_t Suppose that (*) For every i < j < k, and every S in F_i and T in F_k there is R in F_j which contains the intersection of S and T. The basic question is: How large can t be??? Let's call the answer f(n). The question is if f(n) is bounded above by a polynomial in n? A positive answer will imply the "polynomial Hiresh conjecture" namely it will imply that every graph of a d-dimensional polytope with n facets had diameter at most a polynomial in n. C) Polymath3 is a collective attempt to solve the above combinatorial problem that takes place over my blog. http://gilkalai.wordpress.com/ I will try to give a self contained elementary lecture on items A), B) and C)

S.I.G.M.A. Seminar
 F-split rings Link: View Poster Speaker: Lance Miller (University of Utah) Time: Friday, October 15, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: This expository talk will introduce basic topics in the study of rings of characteristic p for p a prime integer. For such rings, one has a natural endomorphism called the Frobenius endomorphism, which is given by the pth power map. With this in mind, we will make the given ring into a nontrivial module over itself. The decomposition of this module gives a lot of information of the types of singularities the ring describes. We will focus on rings where the Frobenius map splits, called F-split rings, which are interpreted as having mild singularities. Comments: Free Pizza (courtesy of Mathematics Department)

Analysis and Probability Seminar
 Uniqueness of Laplacian and Brownian motion on Sierpinski carpets Link: View Poster Speaker: Alexander Teplyaev (University of Connecticut) Time: Friday, October 15, 2010 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: Up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of the Brownian motion is uniquely determined and the Laplacian is well defined. This is a joint work with Martin Barlow, Rich Bass and Takashi Kumagai.

PDE and Differential Geometry Seminar
 Regularity results for the mean curvature flow Link: View Poster Speaker: Nam Le (Columbia University) Time: Monday, October 18, 2010 at 3:30 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk, we will present some joint results on the mean curvature flow with Natasa Sesum. We will show that if the flow is a type I flow then the mean curvature controls the flow in the sense that the blow up of the second fundamental form cannot occur if the mean curvature is uniformly bounded. In the case of surfaces, we will show that the mean curvature controls the flow provided that either the Multiplicity One Conjecture holds or the Gaussian density is less than two. When the mean curvature of our flow blows up, we will also give its (sharp) blow-up rate.

PDE and Differential Geometry Seminar
 On the best constant in the Moser-Aubin-Onofri inequality on S^2 Link: View Poster Speaker: Nassif Ghoussoub (UBC) Time: Tuesday, October 19, 2010 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Let S^2 be the 2-dimensional unit sphere and let J_{alpha} denote the nonlinear functional on the Sobolev space H^{1,2}(S^2) defined by J_{alpha}=frac{alpha}{16pi} int_S^2 | nabla u|^2 d{mu}_0+frac{1}{4pi}int_S^2 u d{mu}_0-ln{int_S^2 frac{e^u}{4pi} d{mu}_0}, where d{mu}_0=sin{theta} d{theta} wedge d{phi} is Lebesgue Measure on S^2 normalized so that int_S^2 d{mu}_0=1. Onofri had established that J_{alpha} is non-negative on H^1(S^2) provided alpha geq 1. In this joint work with C-S. Lin, we show that if J_{alpha} is restricted to those u in H^1(S^2) that satisfies the Aubin condZition: int_{S^2}e^u x_j d{mu}_0=0 for all 1 leq j leq 3, then the same inequality continues to hold (i.e., J _{alpha}(u) geq 0) whenever alpha geq 2/3-epsilon_0 for some epsilon_0 > 0. The question of Chang-Yang on whether this remains true for all alpha >1/2 remains open.

Colloquium
 On the best constant in the Moser-Aubin-Onofri inequality on S^2 Link: View Poster Speaker: Nassif Ghoussoub (University of British Columbia) Faculty Sponsor:Gui Time: Tuesday, October 19, 2010 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: http://www.math.uconn.edu/~khlee/ghoussoub.pdf Comments: Notice the unusual time.

Algebra Seminar
 An introduction to wall-crossing Link: View Poster Speaker: Arend Bayer (University of Connecticut) Time: Tuesday, October 19, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk, I will explain why algebraic geometers got interested in wall-crossing, explain the phenomenon, and introduce some of the techniques used to study it. Examples will include quivers, characteristic p situations, and (time permitting) a classical formula in combinatorics.

 Quantum affine algebras, part 2 Link: View Poster Speaker: Kyu-Hwan Lee (University of Connecticut) Time: Wednesday, October 20, 2010 at 12:00 pm Place: MSB 117 (UConn - Storrs)

 Derived equivalences Link: View Poster Speaker: Lucas David-Roesler (University of Connecticut) Time: Wednesday, October 20, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 The geometry behind solution formulas Link: View Poster Speaker: Arend Bayer (University of Connecticut) Time: Wednesday, October 20, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Everybody knows the solution formula for quadratic equations. Hardly anyone knows the same formula for degree 3 or 4 polynomials. And nobody knows a solution formula for degree 5 polynomials. It turns out that these formulas have a beautiful underlying geometry, once we are willing to work with complex numbers rather than real numbers. Comments: Free Refreshments -- Email: uconnmathclub@gmail.com -- "Like" the UConn Math Club page on Facebook!

S.I.G.M.A. Seminar
 A not-so-long survey of LaTeX Link: View Poster Speaker: Ben Salisbury (University of Connecticut) Time: Friday, October 22, 2010 at 2:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Have you ever wondered how to make your own commands in LaTeX? How about your own package or class file? Have you ever agonized over the page layout or headers in your document? Do you know that there is a package designed to create graphics inside your LaTeX code? Do you still use powerpoint for math related presentations? I plan to address these questions (and hopefully some more) in this week's episode of the S.I.G.M.A. seminar. Comments: Free Snacks (courtesy of Mathematics Department)

Analysis and Probability Seminar
 Criticality of the Abelian Sandpile Model on converging sequences of cacti graphs Link: View Poster Speaker: Michel Matter (Université de Genève) Time: Friday, October 22, 2010 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: We study the statistical-physics Abelian Sandpile Model on converging sequences of finite graphs. The main mathematical question about this model is to prove its criticality -- the correlation between sites situated far away from each other is high -- what is typically done by exhibiting, asymptotically, a power-law decay of various statistics. We consider the model on cacti graphs (separable graphs with cycles as blocks) converging to one-ended limits with respect to Hausdorff-Gromov topology. Interesting examples are provided by covering sequences of (Schreier) graphs arising from self-similar actions by automorphisms of rooted trees. The projective limit of such an inverse system corresponds to the action on the boundary of the tree and its connected components are the (infinite) orbital Schreier graphs of the action. They can be approximated by finite rooted graphs using Hausdorff-Gromov convergence. In particular, we consider the case of the Basilica group acting by automorphisms on the binary rooted tree in a self-similar fashion. We show that the Abelian Sandpile Model on the limit Schreier graphs of the Basilica group is critical almost everywhere with respect to the uniform distribution on the boundary of the tree.

PDE and Differential Geometry Seminar
 Weak solution to Yang-Mills Flow in Dimension n geq 4 Link: View Poster Speaker: Weidong Yin (University of Connecticut) Time: Monday, October 25, 2010 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk, I will present some result on Yang-Mills Flow. In Michael Struwe’s paper ‘The Yang-Mills Flow in Four Dimensions’, he showed short time existence of weak solution to Yang-Mills Flow on a vector bundle over a closed Riemannian manifold M^{4} with W^{1,2} initial date. I basically follow his idea, and show short time existence of weak solution to Yang-Mills Flow with W^{2-n/4, n/2} initial date over a closed manifold M with dimension n geq 4.

Logic Seminar
 Definability and Automorphisms of the C.E. Sets Link: View Poster Speaker: Rachel Epstein (Harvard) Time: Monday, October 25, 2010 at 5:15 pm Place: MSB 403 (UConn - Storrs) Abstract: Definability is one of the fundamental themes of computability theory. We examine the structure of the computably enumerable (c.e.) sets under set inclusion. The problem of which classes of degrees are definable in this structure has been an important topic of study in computability theory. In particular, it has been shown that all upward-closed jump classes (such as high, nonlow2, etc.) are definable except for the nonlow degrees, which are not definable. To show that the nonlow degrees are not definable, we use automorphisms, which we build on trees of strategies. We will discuss the history of the problem and some of the ideas of the proof.

Algebra Seminar
 Graded algebras with quartic growth associated to P^1xP^1 Link: View Poster Speaker: Susan Sierra (Princeton University) Time: Tuesday, October 26, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: It is known that a noncommutative coordinate ring of a projective surface, if noetherian, must have cubic or quintic growth; more formally, such an algebra must have Gelfand-Kirillov dimension 3 or 5. Such an algebra is an example of a so-called birationally commutative projective surface. In contrast, birationally commutative projective surfaces of Gelfand-Kirillov dimension 4 were conjectured by Rogalski and Stafford not to exist. We show this conjecture is false and construct a large family of counterexamples. Our construction uses a sequence of ideal sheaves on P1xP1, and our results include improvements in bounds for the regularity of such sheaves.

 Derived equivalences II Link: View Poster Speaker: Lucas David-Roesler (University of Connecticut) Time: Wednesday, October 27, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

 Quantum affine algebras, part 3 Link: View Poster Speaker: Ryan Kinser (University of Connecticut) Time: Wednesday, October 27, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 Grad school discussion panel Link: View Poster Speaker: Various people (University of Connecticut) Time: Wednesday, October 27, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Comments: Free Refreshments -- Email: uconnmathclub@gmail.com -- "Like" the UConn Math Club page on Facebook!

Colloquium
 Super-Brownian Motion and Critical Random Systems Link: View Poster Speaker: Ed Perkins (UBC/University of Connecticut) Faculty Sponsor:Rich Bass Time: Thursday, October 28, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Brownian motion arises as a universal limiting object for sums of small independent critical (mean zero) contributions; super-Brownian motion arises as a universal limiting object for populations undergoing migration and critical reproduction. It can be used to describe the large scale behaviour of epidemic models, competing species models in ecology and evolutionary game theory, percolation models at criticality, and frequencies of genotypes.

S.I.G.M.A. Seminar
 Embeddings of toric varieties Link: View Poster Speaker: Milena Hering (University of Connecticut) Time: Friday, October 29, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: An algebraic variety is a geometric object that can be described as the zero set of finitely many polynomial equations. I will talk about a special class of algebraic varieties, called toric varieties. A lattice polytope is the convex hull of finitely many points with integer coordinates. I will describe how a lattice polytope gives rise to a toric variety and finish with some results about embeddings of toric varieties. Comments: Free Nibbles (courtesy of Mathematics Department)

Analysis and Probability Seminar
 Dirichlet forms and derivations on fractals Link: View Poster Speaker: Luke Rogers (University of Connecticut) Time: Friday, October 29, 2010 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: The classical Dirichlet energy is the L^2 norm of the gradient of a function. Its study was initially motivated by problems from physics. There is also an abstract notion of a Dirichlet energy on a space of functions, and it is natural to wonder to what extent such an energy may be thought of as an integral of some sort of "gradient". This question has been studied in a number of different ways. The approach I will discuss is from work of Cipriani and Sauvageot, who introduced an algebraic structure that captures the Leibniz (product rule) property of a gradient and is endowed with a Hilbert norm corresponding to the energy. I will describe recent work with Sasha Teplyaev and Marius Ionescu in which we give a concrete description of this algebraic structure on certain types of fractal sets and use this to give simple proofs of some results about Fredholm modules in this context. Note: Ron Blei was originally scheduled to give the talk on this date. His talk will now be on November 12th.

Logic Seminar
 An introduction to o-minimal structures and their applications Link: View Poster Speaker: Alex Wilkie (University of Manchester) Time: Monday, November 1, 2010 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: I shall introduce the theory of o-minimal structures as a possible rigorous framework for Grothendieck's idea of "tame topology". I shall present some of the main finiteness theorems for certain ("definable") subsets of Euclidean space and conclude with an application concerning the counting of rational points on transcendental analytic sets.

PDE and Differential Geometry Seminar
 Axial Symmetry of Some Entire Solutions of Nonlinear Elliptic Equations Link: View Poster Speaker: Changfeng Gui (University of Connecticut) Time: Tuesday, November 2, 2010 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk, I will present some recent results on the axial symmetry of certain entire solutions which are anisotropic.The type of solutions includes stationary solutions for nonlinear Schrodinger equation, saddle solutions and traveling wave solutions for Allen-Cahn equations.

Algebra Seminar
 Enriques surfaces that fail to satisfy the local-to-global principle. Link: View Poster Speaker: Bianca Viray (Brown University) Time: Tuesday, November 2, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We study Enriques surfaces that have a point over every completion Q_v of Q, but no Q-rational points. When this phenomenon occurs in rational surfaces or curves, it is (conjecturally) always accounted for by an algebraic Brauer-Manin obstruction. However, this is not necessarily the case for Enriques surfaces. We construct an Enriques surface with no algebraic Brauer-Manin obstruction, yet still fails to have Q-rational points. We explain how, in our particular example, there is an obstruction coming from the K3 double cover of the Enriques surface. This is joint work with Anthony V'arilly-Alvarado

 Cluster automorphisms Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Wednesday, November 3, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

 Nakajima Quiver Varieties Link: View Poster Speaker: Milena Hering (University of Connecticut) Time: Wednesday, November 3, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 Eigenvalue data on the Sierpinski Carpet Link: View Poster Speaker: Matt Begué (University of Connecticut) Time: Wednesday, November 3, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Much work has been done studying the Laplacian operator on fractals in the past two decades. Recently, research was done on the fractal known as the Sierpinski Carpet, the two dimensional analogue of the Cantor Set. Some of the results from this research will be presented. We will discuss the construction of the Sierpinski Carpet, the construction of the Laplacian, and two important characteristics of the Laplacian's eigenfunctions known as refinement and miniaturization. Comments: Free Refreshments -- uconnmathclub@gmail.com -- "Like" the UConn Math Club page on Facebook!

S.I.G.M.A. Seminar
 Large Lectures in Calculus: A Challenge for Teaching and Research Link: View Poster Speaker: Amit Savkar and Fabiana Cardetti (University of Connecticut) Time: Friday, November 5, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: For the past three years there has been a shift at the University of Connecticut in the teaching of the traditional calculus courses. These courses are now taught in large lectures of 180 to 200 students with several smaller discussion classes. This change has encouraged many instructors to explore the use of technology to help engage students in their learning in-class and outside of it. This year we received a grant from the Provost's office to enhance the learning experience in Calculus 1 (Math 1131) by using technology. The purpose of this talk is twofold: first, to show you the three tools that were developed with these funds to improve the instructors' ability to reach the students. Second, to give an overview of the research study, as well as present some of the challenges in conducting it. Comments: Free Nibbles (courtesy of Mathematics Department)

Analysis and Probability Seminar
 Energy representation of path groups Link: View Poster Speaker: Maria Gordina (University of Connecticut) Time: Friday, November 5, 2010 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: First, we will look at how a quasi-invariant measure on a Lie group induces a unitary representation. Then we will see how this idea can be applied to the group of paths in a Lie group. In the case the Girsanov type quasi-invariance for a Lie group-valued Brownian motion is being used. We will see how questions in stochastic analysis or analysis can be translated into a representation theory language. The results are based on the joint work with S. Albeverio, B. Driver and A.M. Vershik, which is an attempt to clean up some of the results and resolve open questions left unanswered in the works of S. Albeverio, R. Hoegh-Krohn, I. M. Gelfand, M. I. Graev, A. M. Vershik and others.

Logic Seminar
 Effective equivalence structures and their isomorphisms Link: View Poster Speaker: Valentina Harizanov (George Washington University) Time: Monday, November 8, 2010 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: We investigate computable equivalence structures, as well as computably enumerable (c.e.) and co-computably enumerable (co-c.e.) equivalence structures. Together with W. Calvert, D. Cenzer, and A. Morozov, we established that a computable equivalence structure A is computably categorical if and only if A has only finitely many finite equivalence classes, or A has only finitely many infinite classes, bounded character, and at most one finite k such that there are infinitely many classes of size k. Moreover, every computably categorical equivalence structure A is relatively computably categorical, that is, A has a c.e. Scott family of existential formulas. We also characterized relatively limit computably categorical equivalence structures as those with finitely many infinite classes or with bounded character. A. Kach and D. Turetsky proved that not all limit computably categorical equivalence structures are relatively limit computably categorical. Together with D. Cenzer and J. Remmel we further studied c.e. and co-c.e. equivalence structures. While any c.e. equivalence structure with infinitely many infinite classes is isomorphic to a computable structure, there are c.e. equivalence structures that are not isomorphic to computable ones. We showed that if c.e. equivalence structures A and B are isomorphic to a computable structure that is relatively limit computably categorical, then A and B are limit computably isomorphic. On the other hand, for every computable relatively limit computably categorical equivalence structure that is not computably categorical, we construct an isomorphic co-c.e. structure that is not limit computably isomorphic to any computable, even. c.e. structure.

Algebra Seminar
 Affine Stanley Symmetric Functions Link: View Poster Speaker: Steven Pon (University of Connecticut) Time: Tuesday, November 9, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We will discuss a class of symmetric functions that model the cohomology of the affine Grassmannian for any classical Lie type. These symmetric functions, while they have geometric implications, are defined combinatorially via a finite subset of the set of affine Weyl group elements for the corresponding type (the set of Pieri factors) and a statistic on this subset. We will define these symmetric functions, relate them to known symmetric functions (including k-Schur functions and Macdonald polynomials) and give some positivity results.

 The Cluster Category of a Marked Surface Link: View Poster Speaker: Ryan Kinser (University of Connecticut) Time: Wednesday, November 10, 2010 at 2:00 pm Place: MSB 117 (UConn - Storrs)

 Cryptic title involving Quiver varieties, perverse sheaves and convolution product Link: View Poster Speaker: Arend Bayer (University of Connecticut) Time: Wednesday, November 10, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

Analysis and Probability Seminar
 Canceled Link: View Poster Speaker: (University of Connecticut) Time: Friday, November 12, 2010 at 3:00 pm Place: MSB 319 (UConn - Storrs)

S.I.G.M.A. Seminar
 An Introduction to Quivers Link: View Poster Speaker: Lucas Roesler (University of Connecticut) Time: Friday, November 12, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Quivers provide a nice algebraic and combinatorial tool for describing the modules over an algebra. We will introduce the basic definitions for the study of quivers and look at the nicest class of quivers for the study of modules, those of Dynkin type. We will see Gabriel's Theorem and time permitted consider some other nice classes of quivers. Comments: Free Food (courtesy of Mathematics Department)

PDE and Differential Geometry Seminar
 Epitaxial thin film growth model and its numerical simulation Link: View Poster Speaker: Cheng Wang (University of Massachusetts Dartmouth) Time: Monday, November 15, 2010 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: A nonlinear PDE model of thin film growth, with or without slope selection, are presented in the talk. A global solution in time with Gevrey regularity is established for the one with slope selection. For the numerical simulation, an idea of convex-concave splitting of the corresponding physical energy is applied, which gives to an implicit treatment for the convex part and an explicit treatment for the concave part. That in turn leads to a numerical scheme with a non-increasing energy. Both the first and second order splittings in time, both the centered difference and the fourth order long stencil difference spatial approximations, will be considered in the work. Some numerical simulation results are also presented in the talk.

Logic Seminar
 Difference randomness Link: View Poster Speaker: Johanna Franklin (Dartmouth) Time: Monday, November 15, 2010 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: Martin-Loef randomness is the most frequently studied randomness notion. It can be characterized easily using initial-segment complexity, betting strategies, and measure theory, and it satisfies many of our intuitions about randomness. However, there is one intuition that it does not satisfy: a Martin-Loef random sequence can have arbitrarily high computational strength. In this talk, I will present a way of characterizing the Martin-Loef random sequences with low computational strength by defining a new randomness notion using the difference hierarchy. This is joint work with Keng Meng Ng.

UConn Math Club
 Mathematical modeling and leukemia Link: View Poster Speaker: Andy Stein (Novartis Institute for Biomedical Research) Time: Monday, November 15, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Every year, roughly 5,000 people in the US are diagnosed with chronic myeloid leukemia (CML), a type of blood cancer. CML is thought to be driven by a small population of leukemic stem cells and while the drug imatinib induces a durable response to therapy in most patients, it is currently unclear whether imatinib reduces the leukemic stem cell burden. Due to the sparsity of stem cells in the bone marrow (1 in 1,000,000 cells) changes in the stem cell population are difficult to observe though direct clinical measurements. We use mathematical models to describe the response dynamics of CML patients undergoing imatinib therapy to infer that the LSCs exhibit a gradual decline over time. In the future, this modeling approach can be used to analyze data from patients who stop imatinib after achieving undetectable levels of the disease in the context of carefully conducted clinical trials, with the goal of assessing (a) the potential impact of imatinib interruption on LSC levels, particularly in those patients who relapse and (b) whether the probability of achieving cure depends on the steepness of response prior to achieving undetectable levels of transcripts or other factors. Comments: Free Refreshments -- uconnmathclub@gmail.com -- "Like" the UConn Math Club on Facebook! Additional Comments: NOTE the special *Monday* meeting

Algebra Seminar
 Selmer groups and their Projectivity. Link: View Poster Speaker: Myoungil Kim (Boston University) Time: Tuesday, November 16, 2010 at 11:00 am Place: MSB 118 (UConn - Storrs) Abstract: We review Selmer groups for elliptic curves and Selmer groups for some related Galois modules. We discuss the behavior of Selmer groups for Galois representations with the same residual representation. R. Greenberg recently obtained various results for the elliptic curves with ordinary reduction. We introduce some of the main results of Greenberg. Then we define some variant Selmer groups for elliptic curves with non ordinary reduction and prove an analogous result.

 Cluster Bases in Affine Cluster Algebras Link: View Poster Speaker: Grégoire Dupont (Université Sherbrooke) Time: Wednesday, November 17, 2010 at 1:00 pm Place: MSB 117 (UConn - Storrs)

 Quiver varieties and cluster algebras Link: View Poster Speaker: Kyungyong Lee (University of Connecticut) Time: Wednesday, November 17, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

S.I.G.M.A. Seminar
 Just What is the Connection Between Physics and Music? Link: View Poster Speaker: George Gibson (University of Connecticut) Time: Friday, November 19, 2010 at 12:45 pm Place: MSB 118 (UConn - Storrs) Abstract: "What we are nowadays hearing of the language of spectra is a true "music of the spheres" within the atom, chords of integral relationships, an order and Harmony that becomes ever more perfect in spite of the manifold variety." - Sommerfeld (1919). From the Neanderthals to Pythagoras, through the Enlightenment, to the development of Quantum Mechanics, physicists have been motivated, inspired, and obsessed by music. Even today, physicists try to describe the natural world in musical terms. This talk will discuss this complex interplay between physics and music and explore just how deep this connection really is. Comments: Free Pizza (courtesy of Mathematics Department)

Algebra Seminar
 Varieties defined by arrangements Link: View Poster Speaker: Giancarlo Urzua (University of Massachusetts - Amherst) Time: Tuesday, November 30, 2010 at 11:00 am Place: MSB 118 (UConn - Storrs) Abstract: I will start describing results concerning algebraic surfaces and arrangements of curves in the context of simply connected geography, and briefly sketch how this may work for 3-folds, pointing out the main obstacles. Then, I will introduce a new class of arrangements of curves which produce a huge class of algebraic surfaces with distinguished properties. Some examples in positive characteristic and connections with effective high inequalities will decorate the talk.

 The Cluster Category of a Marked Surface II Link: View Poster Speaker: Ryan Kinser (University of Connecticut) Time: Wednesday, December 1, 2010 at 2:00 pm Place: MSB 117 (UConn - Storrs)

 t-analogs of q-characters Link: View Poster Speaker: Kyungyong Lee (University of Connecticut) Time: Wednesday, December 1, 2010 at 3:05 pm Place: MSB 117 (UConn - Storrs)

UConn Math Club
 Truth, Provability, and Counting: What is mathematical logic all about? Link: View Poster Speaker: Paul Ellis (University of Connecticut) Time: Wednesday, December 1, 2010 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Mathematical logic investigates some of the fundamental questions in mathematics. What does it mean for a statement to be true? What does it mean for a statement to be provable? If a statement is provable, is it true? (We'd hope so!) If a statement is true is it provable? (It depends.) If time permits, we will talk about Cantor's Continuum Hypothesis, which asks: Is there a set of real numbers that is smaller than the set of reals, yet bigger than the set of rationals? (Answer: It depends!) Also, what does the previous question even mean? Comments: Free Refreshments -- uconnmathclub@gmail.com -- "Like" the UConn Math Club on Facebook!

S.I.G.M.A. Seminar
 Algebra, Meet Geometry! Link: View Poster Speaker: Arend Bayer (University of Connecticut) Time: Friday, December 3, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: I will explain how seemingly algebraic questions on polynomials have an underlying geometric background, and how methods from geometry and topology can yield answers to such algebraic questions. The first example is an extremely classical one: Is there a solution formula for an equation x5 + a x4 + b x3 + d x2 + e x + f = 0 of degree 5? The underlying geometry will relate this question to covering spaces, the symmetric group and the braid group. The second example is "Fermat's theorem for polynomials": There are (essentially) no polynomials p(t), q(t), r(t) satisfying the equation p(t)n + q(t)n = r(t)n for n ≥ 3. This question may seem peculiar at first, but studying the underlying geometry leads to the theory of algebraic curve, and an extremely general answer. Comments: Free Pizza (courtesy of Mathematics Department)

PDE and Differential Geometry Seminar
 Comparison of Numerical Solutions of Time-Fractional Reaction–Diffusion Equations Link: View Poster Speaker: Muhammet Kurulay (University of Connecticut) Time: Monday, December 6, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk, we will compare numerical solutions for time-fractional reaction–diffusion equation using variation iteration, homotopy perturbation, adomian decomposition and differential transform methods. The fractional derivatives are described in the Caputo sense. The methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional partial differential equations. The approach rests mainly on two-dimensional differential transform method which is one of the most efficient from approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. An example is given to demonstrate the effectiveness of the present method

Logic Seminar
 Cardinal invariant properties of countable Borel equivalence relations Link: View Poster Speaker: Scott Schneider (Wesleyan University) Time: Monday, December 6, 2010 at 4:45 pm Place: Exley Science Center 618 (Wesleyan University) Abstract: Boykin and Jackson have shown that the bounding number, b, can be used to define a property of countable Borel equivalence relations that is relevant to the unions problem for hyperfinite relations. In fact, many other cardinal invariants of the continuum can be used in an analogous manner to define "Borel cardinal invariant" properties of countable Borel equivalence relations. In this talk, we introduce these new properties and examine some of the basic relationships that hold between them, thus linking the study of countable Borel equivalence relations with that of cardinal invariants of the continuum. In particular, we show that the property corresponding to the splitting number s is equivalent to smoothness.

Algebra Seminar
 Hamiltonian Torus Actions on Orbifolds Link: View Poster Speaker: Tomoo Matsumura (Cornell University) Time: Tuesday, December 7, 2010 at 11:00 am Place: MSB 118 (UConn - Storrs) Abstract: When a symplectic manifold M carries a Hamiltonian torus R action, the injectivity theorem states that the R-equivariant cohomology of M is a subring of the one of the fixed points and the GKM theorem allows us to compute this subring by only using the data of 1-dimensional orbits. The main results I will talk about are a generalization of this technique to Hamiltonian torus actions on orbifolds" and an application to the computation of the equivariant cohomology of compact toric orbifolds. I will start with a brief discussion on orbifolds and Hamiltonian actions. If time allows, I will introduce the equivariant Chen-Ruan cohomology ring which is a symplectic invariant of the action on the orbifold and explain the injectivity/GKM theorem for this ring.

Colloquium
 Compact moduli spaces of algebraic surfaces Link: View Poster Speaker: Jenia Tevelev (University of Massachusetts-Amherst) Faculty Sponsor:Bayer Time: Thursday, December 9, 2010 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: It is fair to say, borrowing a phrase from Max Noether, that the moduli space of algebraic curves was created by God but the moduli space of algebraic surfaces was designed by the Devil. While the former space has a beautiful well-understood geometry, the latter space is known, among other things, to possess literally arbitrary singularities! However, for many surfaces we have a good idea how the moduli spaces and their compactifications look like. I will give a survey of some results in this direction.

S.I.G.M.A. Seminar
 Inversion of Matrices via Simple Graph Manipulations Link: View Poster Speaker: Pavel Zhlobich (University of Connecticut) Time: Friday, December 10, 2010 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The intimate connection between matrices and polynomials is very well studied. Recall, for instance, Perron-Frobenius Theorem for nonnegative matrices. In our talk we will focus on the relation between polynomial Vandermonde matrices (arising in interpolation and other related problems) and the so-called Signal Flow Graphs (SFG) widely used in System Theory and Digital Filtering. Recently many fast and stable algorithms of inversion of polynomial Vandermonde matrices were developed for different polynomial systems such as monomials, real orthogonal polynomials, polynomials orthogonal on the unit circle. We will show how to unify and generalize these results using the language of SFG. The outcome will be an algorithm of inversion of polynomial Vandermonde matrix with the complexity of order N2 for ANY polynomials satisfying short recurrence relations. Comments: Free Pizza (courtesy of Mathematics Department)