University at Albany


To receive updates to the colloquium schedule by email, email Marco Varisco. 
The colloquium usually meets on Friday at 3:00 pm in room ES 143.

SPECIAL COLLOQUIUM to Celebrate Mark Steinberger’s 65th Birthday

Peter B. Shalen (University of Illinois at Chicago)
Three-Dimensional Topology and the Enumeration of Arithmetic Groups

Friday, September 4, 2015
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract. Quaternion algebras are natural objects in number theory, analogous to number fields. An arithmetic lattice in a quaternion algebra is roughly analogous to the group of units in the integers of a number field. Remarkably, certain arithmetic lattices (those defined over fields with exactly one complex place, and ramified at all real places) can be studied via the geometry and topology of 3-manifolds, or more generally (if they have elements of finite order) of objects called 3-orbifolds.

The manifolds (or orbifolds) associated with arithmetic lattices are hyperbolic manifolds, locally modelled on the 3-dimensional non-Euclidean geometry of Gauss, Bolyai and Lobachevsky (or quotients of the latter by finite groups). In particular, each of these manifolds has a well-defined volume.

A theorem of Borel’s asserts that for any positive real number V, there are at most finitely many arithmetic lattices of covolume at most V. Determining all of these for a given V is algorithmically possible thanks to work by Chinburg and Friedman, but appears to be impractical except for very small values of V, say V = 0.41. (The smallest covolume of a hyperbolic 3-orbifold is about 0.39.) It turns out that the difficulty in the computation for a larger value of V can be dealt with if one can find a good bound on dim H_1(O,Z/2Z), where O is a hyperbolic 3-orbifold of volume at most V.

In the case of a hyperbolic 3-manifold M, not necessarily arithmetic, joint work of mine with Marc Culler and others gives good bounds on the dimension of H_1(M,Z/2Z) in the presence of a suitable bound on the volume of M. In this talk I will discuss some analogous results for hyperbolic 3-orbifolds, and the prospects for applying results of this kind to the enumeration of arithmetic lattices. A feature of the work that I find intriguing is that while it builds on my geometric work with Culler, the new ingredients involve primarily purely topological arguments about manifolds—the underlying spaces of the orbifolds in question—and have a classical, combinatorial flavor.

Next lecture:

September 18
Amanda Folsom (Amherst College)

Earlier colloquia and abstracts:

May 1
Eric Sommers (UMass Amherst)

April 24
Fourth Annual Maheshwari Colloquium
Jill Pipher (Brown University, ICERM)

April 17
Bogdan Ion (University of Pittsburgh)

April 10
Kyu-Hwan Lee (University of Connecticut)

February 27
Anna Mazzucato (Penn State)

John Schmitt (Middlebury College)
Warning’s Second Theorem with Restricted Variables

Friday, January 30, 2015
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: The polynomial method is a successful and promising approach for solving combinatorial problems. We will discuss this method via a theorem of Alon and Furedi and offer a new (and short) proof of a number-theoretic theorem of Ewald Warning from 1935, which concerns the number of zeros of a polynomial system over a finite field. We also offer a broad generalization of Warning’s theorem. Further, we will discuss applications of this generalization to various zero-sum problems in additive combinatorics.
This is joint work with Pete L. Clark (U. Georgia) and Aden Forrow (M.I.T.)

Bernard Leclerc (Université de Caen, France)
Kirillov-Reshetikhin Modules and Their q-Characters

Monday, November 3, 2014
10:25–11:25 in ES-139

Abstract. Kirillov-Reshetikhin modules are a class of irreducible finite-
dimensional representations of quantum affine algebras (or Yangians). Ini-
tially introduced in mathematical physics in relation with certain integrable
models, they appear as the most “accessible” irreducible representations. I
will explain recent new methods to describe their q-characters: (1) an algo-
rithmic method which allows to calculate them by successive approximations;
(2) a geometric method which expresses them in terms of Euler characteristics
of Grassmannians of submodules for a quiver with potential. Both methods
come from the interpretation of the q-characters of Kirillov-Reshetikhin mod-
ules as cluster variables in the Grothendieck ring. They work in a uniform
way for all untwisted quantum affine algebras. This is joint work with David
Hernandez (arXiv:1303.0744).

David Cruz-Uribe (Trinity College)

The Rise, Fall and Rebirth of the Muckenhoupt-Wheeden Conjectures

Friday, November 7, 2014
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Kirill Zainoulline (University of Ottawa)

Oriented Equivariant Cohomology, Formal Group Laws, And Generalized Schubert Calculus

Friday, October 10, 2014

3:00 p.m. in ES-143

(tea & coffee at 2:30 p.m. in ES-152)

Abstract. Oriented equivariant cohomology theories and the associated formal groups laws have been a subject of intensive investigations since the 60’s, mostly inspired by the theory of complex cobordism in topology. In the present talk we discuss several recent developments in the study of algebraic analogues of such theories, e.g., algebraic cobordism of Levine-Morel or alge-braic elliptic cohomology, of projective homogeneous varieties. In particular, we address the problem of constructing the Schubert and the Bott-Samelson classes for such theories.

Man-Duen Choi (University of Toronto)
What On Earth Does A Quantum Computer Mean?

Friday, March 7, 2014
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: Suddenly, there arises the new era of real quantum computers, with all sorts of information process in the setting of non-commutative analysis. From the point of view of a pure mathematician, I will explain how matrix method can be used intensively in the recent development of quantum information joining quantum mechanics and computer science. This is an expository talk with rudiments of matrix theory; no background knowledge of physics or computer will be assumed.

Massimiliano Pontil (University College London)
Learning from Data

Monday, February 17, 2014
4:15 p.m. in ES-143
(tea & coffee at 3:15 p.m. in ES-152)

Abstract: Machine learning is an exciting and rapidly expanding area of computer science with cross links to computational mathematics and statistics and to the emerging fields of big data and data science. Machine learning has expanded dramatically during the past fifteen years or so, becoming a mature area with rich theory and applications. Modern learning techniques draw substantial ideas and inspirations from numerous areas of mathematics. Approximation theory, functional analysis and numerical optimization provide important tools to formalise the problem of learning from data. At the same time, probability and statistics offer important concepts which can be used to bound the performance (generalization error) of a learning algorithm in a principled way. A main goal of machine learning is to learn functional relationships and representations from multiple and high dimensional data sources. In this talk, I will give an overview of recent progress on this problem, highlighting the interplay between ideas and tools from maths, statistics and computer science. A crucial step for effective and efficient learning is to incorporate prior knowledge on the model underlying the data. I will present a comprehensive framework to achieve this goal, which allows us to incorporate constraints in the learning problem using certain convex regularization functionals. They drive the learning algorithm towards functions which fit the data well and satisfy the desired properties. In particular, I will describe families of norms which encourage smoothness and sparsity, as well as relationships between multiple functions. Furthermore I will discuss extensions of these ideas to learn tensors, using multilinear algebra. Finally, I will present numerical simulations which illustrate the practical value of this framework in applications arising in various domains, including user modeling, computer vision and affective computing.

Jin Wang (Old Dominion University)
Computation and Analysis of Multiphase Fluid Flows with Moving Interfaces

Thursday, February 13, 2014
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: Multiphase fluid flows with moving interfaces occur in a wide range of natural and technological phenomena. Owing to their strong nonlinearity and inherent multiphysics, our current understanding of the fundamental mechanisms involved remains limited. In the first part of this talk, we focus our attention on the interfacial motion between two incompressible and viscous fluids. After a short discussion of some results from linear analysis, we present a novel numerical method with high accuracy for the simulation of the fully nonlinear interfacial flow. We discuss in detail the algorithm development, simulation results, and treatment and analysis of the numerical data. With this algorithm, traveling waves, such as Stokes waves, can be followed sufficiently in time to reveal the effects of small viscosity. The numerical observation and data analysis are then justified by deriving a formal asymptotic theory. In the second part of this talk, we discuss several related studies, particularly the fluid-structure interaction problems, and their many interdisciplinary applications.

Brett Wick (Georgia Institute of Technology)
The Corona Theorem

Friday, November 8, 2013
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: Carleson’s Corona Theorem from the 1960’s has served as a major motivation for many results in complex function theory, operator theory, and harmonic analysis. In a simple form, the result states that for N bounded analytic functions f1,...,fN on the unit disc such that inf |f1|+···+|fN| >= d > 0 it is possible to find N other bounded analytic functions g1,...,gN such that f1g1+···+fNgN = 1. Moreover, the functions g1,...,gN can be chosen with some norm control.
In this talk we will discuss some generalizations of this result to certain vector-valued functions and connections with geometry and to function spaces on the unit ball in several complex variables.

Peter Shalen (University of Illinois at Chicago)
Quantitative Mostow Rigidity

Friday, October 25, 2013
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: A hyperbolic n-manifold is a space locally modeled on an n-dimensional non-Euclidean space in which the sum of the angles of a triangle is less than π. Equivalently, it is a Riemannian manifold of constant sectional curvature −1. It is a special case of the Mostow Rigidity Theorem that for n > 2 a compact hyperbolic n-manifold M is determined up to isometry by its fundamental group. In particular any geometrically defined invariant of M, such as its volume or diameter, is a topological invariant of M (and in fact an algebraic invariant of π_1(M)). This raises the fascinating question of how to relate these geometrically defined quantities to more classical topological invariants of M, such as the rank of its first homology group H_1(M). While qualitative connections of this kind are relatively easy, making them quantitative can be quite challenging; for example, it is not hard to obtain a linear bound for the rank of H_1(M) in terms of the volume of M, but the best constant of linear growth is not known. I will explain how I have been bringing deep topological, geometric and analytic techniques to bear on this problem for the case n = 3. In particular, techniques of 3-dimensional topology from the mid-20th century play a surprising role. Some of the work I will describe is joint work with Marc Culler and others.

Greg Kuperberg (University of California, Davis)
What is quantum probability?

Friday, September 20, 2013
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: Quantum mechanics is difficult for many people to understand because it is difficult to believe. The heart of the problem is quantum probability, which is an entirely rigorous theory; nonetheless even many working mathematicians have trouble believing it. (Quantum field theory is far from entirely rigorous, but that is a different topic.) In the past 15 years or so, work in quantum probability has greatly expanded in the guise of quantum computation and quantum information theory. In this talk, I will discuss some of the ideas of quantum probability, quantum computation, and quantum information, using the language of pure mathematics.


Holger Reich (Freie Universität Berlin, Germany)
GL(n,Z) and Algebraic K-Theory

Friday, September 13, 2013
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: The Farrell-Jones conjecture gives a conjectural description of the algebraic K-theory of the group ring of an infinite group G. The conjecture has important consequences in geometric topology. The talk will give an elementary introduction to the conjecture and report on the case G=GL(n,Z).

Željko Čučković (University of Toledo)

Compactness of Hankel Operators on Convex Domains


Friday, March 29, 2012
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: We are interested in the following question: How does compactness of (products of) Hankel operators on the Bergman space relate to the boundary geometry of domains in C^n? We will present some previous results on convex domains as well as our current work on convex Reinhardt domains in C^2.

Avraham Soffer (Rutgers University)
Solitons and Nonlinear Partial Differential Equations

Friday, February 22, 2012
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: This is a general talk about the notion of Soliton and its importance in understanding Dispersive Wave Equations. I will describe the existence and stability of solitons, then the modern theory of Asymptotic Stability and finally open problems and conjectures.

Anders Buch (Rutgers University)
Gromov-Witten Invariants and Puzzles

Friday, November 30, 2012
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: The development of algebraic geometry has been motivated by enumerative geometric questions where one asks for the number of geometric figures of some type that satisfy a list of conditions. For example, the Gromov-Witten invariants of a flag manifold count the number of curves that meet a list of Schubert varieties in general position. I will focus on the (3 point, genus zero) Gromov-Witten invariants of Grassmannians, which are known to be special cases of the multiplicative structure constants of the Schubert polynomials studied in combinatorics. A conjecture of Allen Knutson asserts that certain Schubert structure constants are equal to the number of triangular puzzles that can be created using a list of puzzle pieces. I will discuss a recent proof of this conjecture, how it leads to a positive combinatorial formula for Grassmannian Gromov-Witten invariants, and generalizations. This talk is based on papers with A. Kresch, L. Mihalcea, K. Purbhoo, and H. Tamvakis.

Friday, November 2, 2012
3:00 p.m. in ES-143
(tea & coffee at 2:30 p.m. in ES-152)

Abstract: During the last couple of decades, writers of both fiction and non-fiction, dramatists, movie directors and television producers have increasingly turned to mathematics and the lives of mathematicians as a fertile source of material. My own career as a research mathematician and enthusiastic reader has led me recently to ponder the possibility of creating a course that engages students in noteworthy mathematical concepts, results or individuals, primarily through literary fiction and fictional biography. The result is a course that I created (and taught) entitled “Mathematics in Literature.” The promotion for the course was the following:

“Do you like to read? Do you like mathematics? Combine your interest in both in a new and stimulating way. Read historical fiction and fictional biography with a focus on historically important mathematics problems, significant mathematicians or fundamental issues involved in the foundations of mathematical certainty. Read and discuss novels with protagonists who are mathematicians or with the narrative thread weaving mathematics and mathematicians into a web of intrigue.”

This talk will discuss various aspects of the course and will include both a sample of readings from the source material and a brief description of the significant mathematical issues unifying most of the material.

Laurent Baratchart (INRIA Sophia Antipolis, France)

Compacts of Minimum Capacity and Rational Approximation

Friday, October 19, 2012
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract: Approximation of holomorphic functions of one variable on compact sets of their analyticity domain is an old issue in function theory. From the possibility of approximation asserted by Runge’s theorem, the emphasis has gradually moved towards error rates and asymptotics for the poles. For (possibly multivalued) functions with singular set of zero capacity, a theory has emerged where certain extremal problems from logarithmic potential theory, of Chebotarev type, play a central role. We shall survey these developments and present some recent results. For instance, best approximants (in various senses) of degree n on a Jordan curve to a function with branchpoints inside the curve converge as n goes large in the complement of the set of smallest Green capacity outside of which the function is single-valued.

Michael J. Hopkins (Harvard University)
Symmetry, Homotopy, and Smooth Manifolds

The Inaugural Maheshwari Colloquium , endowed in honor of Man Mohan and Asha Devi Maheshwari by our alumnus Raj Maheshwari ’83.

Friday, April 20, 2012
3:30 p.m. in Lecture Center 4
(Refreshments will be served at 2:45 p.m.)

For details, see

Alex Iosevich (University of Rochester)
Multi-Linear Operators, Distribution of Simplexes, and Geometric Combinatorics

Friday, March 23, 2012
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract: We are going to study several Erdős type problems on the distribution of simplexes in finite subsets of the Euclidean space using multi-linear operator bounds, geometric measure theory, and a variety of conversion mechanisms. The talks should be accessible to a wide audience.

Victor Ivrii (University of Toronto)
100 Years Of Weyl’s Law

Friday, February 17, 2012
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract: In 1911–1912 Hermann Weyl published two papers (more followed) describing the distribution of the eigenvalues of the Dirichlet Laplacian in a bounded domain. These were among the first publications by Weyl and a new exciting field of mathematics was created.
I will discuss:
* Weyl law with sharper remainder estimates (in particular, Weyl conjecture);
* Generalized Weyl law;
* When the generalized Weyl law works and when it does not and how it
should be modified;
* What should be used instead of the eigenvalue counting function when the
spectrum is not necessarily discrete;
* Weyl law and Thomas-Fermi theory.

Joshua Isralowitz (University of Göttingen)
Compactness of operators in the Toeplitz algebra of the Fock space

Thursday, February 9, 2012
4:15 p.m. in ES-143 (tea & coffee at 3:30 p.m. in ES-152)

Abstract. In 2004 D. Suarez showed that a bounded operator on the Bergman space of the ball is compact if and only if the operator is in the Toeplitz algebra and the Berezin transform of the operator vanishes at the boundary of the ball. In this talk, I will discuss an even stronger version of this result for the Fock space. This is joint work with W. Bauer.

David Anderson (University of Washington)
Okounkov bodies: from algebraic to convex geometry

Tuesday, February 7, 2012
4:15 p.m. in ES-143 (tea & coffee at 3:30 p.m. in ES-152)

Abstract. Building on earlier work of Okounkov, in 2008 Kaveh, Khovanskii, Lazarsfeld, and Mustata showed how to construct a convex body in n-dimensional Euclidean space naturally associated to a line bundle on an n-dimensional algebraic variety, in such a way that the convex geometry of this body reflects algebro-geometric properties of the line bundle.  This construction generalizes a well-understood correspondence between toric varieties and polytopes: when one starts with a toric variety and an equivariant line bundle, the associated convex body is the polytope arising from the yoga of toric geometry.
After describing the history and construction of these so-called “Okounkov bodies” from an elementary point of view, I will explain how the toric correspondence can be made tighter: under the right conditions, the Okounkov body is a polytope, and the variety in question deforms to a toric variety with the same Okounkov body.  The toric correspondence provides a remarkably useful bridge between several branches of mathematics, and we will see connections between geometry, algebra, combinatorics, and representation theory.

Artem Pulemotov (University of Chicago)
Geometric flows on manifolds with boundary

Thursday, February 2, 2012
4:15 p.m. in ES-143 (tea & coffee at 3:30 p.m. in ES-152)

Abstract. Geometric flows are partial differential equations that describe evolutions of geometric objects. They are typically used to tackle problems in topology, mathematical physics, and several other fields. The canonical example of a geometric flow is the heat equation on a Riemannian manifold. In the first part of the talk, we will discuss the fundamental features of this equation. We will also speak about two estimates for its positive solutions on manifolds with boundary. A more contemporary example of a geometric flow is the Ricci flow for a Riemannian metric. It is mostly famous for its role in the proof of the Poincaré conjecture. The second part of the talk will be devoted to the main features and the behavior of the Ricci flow on manifolds with boundary. Towards the end, we will give a brief overview of related problems.

Liz Vivas (Purdue University)
Dynamics of holomorphic self-maps near a fixed point

Tuesday, January 31, 2012
4:15 p.m. in ES-143 (tea & coffee at 3:30 p.m. in ES-152)

Abstract. The local dynamics of holomorphic self-maps of C^n around a fixed point has been an object of study since the time of Schröder, Fatou and Julia. In this talk we will explain the results known for n=1 and the partial known results for n>1. We will focus in the case n=2 and of maps tangents to the identity, that is, when the derivative of our self-map at the fixed point is the identity. In this case the usual tools of linearization introduced by Poincaré are not possible to use and some new techniques are required.

Daniel Ramras (New Mexico State University)
Spaces of Representations and the Topological Atiyah-Segal Transformation

Friday, January 27, 2012
4:15 p.m. in ES-143 (tea & coffee at 3:30 p.m. in ES-152)

Abstract. The relationship between representations of a group and vector bundles was first studied by Atiyah and Segal in the early 1960s, via a construction that associates a vector bundle to each representation. Early work in this direction focused on finite groups, or compact Lie groups. When one considers infinite discrete groups, such as the fundamental group of a closed manifold, continuous families of representations come into play. In particular, the Atiyah-Segal construction may be generalized so as to associate a vector bundle to each such family. In this talk, I’ll explain how methods from differential geometry, algebraic geometry, and homotopy theory can be combined to study this construction, yielding concrete results about vector bundles over familiar spaces such as surfaces.

Thomas Banchoff (Brown University)
Triple Points of Surfaces, Immersed and Non-Immersed

*Wednesday*, January 25, 2012
*4:15* p.m. in *ES-241* (tea & coffee at 3:45 p.m. in ES-152)

Abstract. Forty years ago the first proofs were published relating the number of triple points of a surface immersed in three-space to the number of handles of the surface. New proofs then appeared including one by Richard Goldstein and Ted Turner that is particularly good for proving an extension of that result for stable mappings with pinch points. The talk will feature computer graphics images and animations.

Allan Greenleaf (University of Rochester)
Resolution of Singularities for Analysts

Friday, November 4, 2011
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract. A basic problem is to describe the zero set of a polynomial or analytic function. In algebraic geometry, resolution of singularities was established by Hironaka in 1964 and has since developed into a powerful collection of methods. In analysis, there is a need for more concrete and effective approaches, allowing one to find numerical invariants of functions near zeros or critical points, such as the critical integrability, sublevel growth and oscillatory indices. I will describe these invariants, how they arise, and outline an analyst-friendly approach to resolution of singularities.
This is joint work with Tristan Collins and Malabika Pramanik.

Mark Shimozono (Virginia Polytechnic Institute and State University)
Parabolic Lusztig q-Analogues and One-Dimensional Sums

Thursday, October 6, 2011
1:15 p.m. in ES-146 (tea & coffee at 12:45 a.m. in ES-152)

Abstract. Parabolic Lusztig q-analogues are a family of polynomials which
include Lusztig’s q-analogues of weight multiplicity, which describe the
intersection cohomology of certain Schubert varieties in the affine flag
manifold. One-dimensional (1d) sums are polynomials which arose in the study
of two-dimensional solvable lattice models and in the Kyoto school’s
construction of crystal graphs for highest weight modules over quantum affine
algebras. We show that for G of classical type there is a subfamily called
stable parabolic Lusztig q-analogues, which coincides with the family of
large-rank limits of 1d sums.
This is joint work with Cedric Lecouvey and Masato Okado.

Alexander Dranishnikov (University of Florida, Gainesville)
Lusternik-Schnirelmann category and the fundamental group

Friday, September 9, 2011
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract. The Lusternik-Schnirelmann category measures the complexity
of manifolds. It gives a low bound for the number of critical points
of any (not necessarily Morse) smooth function. It is known that for
n-manifolds the LS-category does not exceed n. The Whitehead theorem
states that for simply connected n-manifolds it does not exceed n/2.
We extend Whitehead’s theorem for spaces with certain fundamental

Paul Loya (Binghamton University, SUNY)
An introduction to Witten’s holonomy theorem

Friday, April 29, 2011
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract: In the 1980’s Daniel Quillen introduced determinant line
bundles and about the same time Edward Witten derived a remarkable
formula for the holonomy of the determinant line bundle of a Dirac
operator using something called the “eta invariant” of Atiyah, Patodi,
and Singer. In the physics literature, the holonomy of the determinant
line bundle is called the “global anomaly". Witten’s derivation was
later made rigorous by Bismut and Freed and also by Cheeger.
In this talk I will give an introduction to eta invariants and
Witten’s holonomy theorem, and then I will discuss recent work
concerning generalizations of this theorem to situations quite
different from the original results. This talk will be suitable for a
general audience.

Tao Qian (University of Macau)
Adaptive Fourier Decompositions (AFDs) and Best Approximation by Rational Functions

Friday, April 8, 2011
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract. The talk will compare three different models of adaptive
Fourier decompositions with illustrative experimental results.
We introduce the problem of best approximation by rational functions
and its connection with the AFDs, as well as some questions in
relation to the algorithm of its solution.

Hara Charalambous (University of Thessaloniki)

Betti fibers for binomial ideals and indispensable complexes

Friday, February 4, 2011
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract: In a polynomial ring we consider ideals generated by
binomials. We study the characterization of minimally generating
sets for such ideals even when Nakayama’s Lemma fails.

Alfonso Montes Rodriguez (University of Sevilla, Spain)

Uniqueness Sets for the Klein-Gordon Equation and the Solution of a
Conjecture of Salem

Friday, November 12, 2010
4:30 p.m. in ES-143 (tea & coffee at 4:00 p.m. in ES-152)
(please notice unusual time)

Patricia Hersh (North Carolina State University)

Combinatorics and Topology of Stratified Spaces

Friday, October 29, 2010
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract: Anders Björner characterized which finite, graded partially
ordered sets (posets) are closure posets of regular CW complexes, and
he also observed that a finite, regular CW complex is homeomorphic to
the order complex of its closure poset. One might therefore hope to
use combinatorics to determine topological structure of stratified
spaces by studying their closure posets; however, it is possible for
two CW complexes with very different topological structure to have the
same closure poset if one of them is not regular. I will discuss a
criterion for determining whether a finite CW complex is regular (with
respect to a choice of characteristic maps); this will involve a
mixture of combinatorics and topology. Along the way, I will review
the notions from topology and combinatorics we will need.  Finally I
will discuss an application: the proof of a conjecture of Fomin and
Shapiro, a special case of which says that the Bruhat cell
decomposition of the neighborhood of the origin in the totally
nonnegative part of the space of upper triangular matrices with 1's on
the diagonal is a regular CW complex homeomorphic to a ball.

Pablo Gonzalez-Vera (University of La Laguna, Spain)

On the Computation of Weighted Integrals: from the real line to the unit circle

Friday, October 22, 2010
3:00 p.m. in ES-143 (tea & coffee at 2:30 p.m. in ES-152)

Abstract: In this talk quadrature formulas to approximately calculate
integrals both on intervals of the real line and the unit circle are
revisited and their basic features exposed. Different connections
between the real line and the unit circle are exploited by showing
that the computation of the quadrature formulas essentially reduce to
the case of the unit circle.

Raul Curto (University of Iowa)
Cubic Column Relations in Truncated Moment Problems

Friday, October 15, 2010
3:00 p.m. in ES-143
(Tea at 2:30 p.m. in ES-152)


Spring 2010

Leonardo Constantin Mihalcea, Baylor University
Quantum K-theory or How to Count Infinitely Many Curves 
Friday, February 5, 2010
4 pm, ES 143
Alex Feingold, Binghamton University
Hyperbolic Weyl Groups and the Four Normed Division Algebras 
Friday, February 12, 2010
3 pm, ES 143
Erik Pedersen, Copenhagen and Binghamton University
Manifolds with universal cover a sphere cross euclidean space 
Friday, March 12, 2010
4:15 pm, ES 143
Jie Xiao, Memorial University
The Minkowski Problem, Old and New 
Friday, April 30, 2010
3:00 pm, ES 143
Drazen Adamovic, University of Zagreb
On rational and C2-cofinite vertex algebras 
Friday, May 7, 2010
3 pm, ES 143



Fall 2009

George Andrews, Penn State University
Lessons from Ramanujan's Lost Notebook 
Wednesday, September 16, 2009 
4:15 pm (note unusual time!), ES 147 

Peter Tingley, MIT
Some combinatorics related to affine sl(n) representation theory 
Friday, October 30, 2009 
3:00 pm, ES 143 

Tao Qian , University of Macao
Adaptive modified Blashke product decomposition (Takenaka Malmquist system ) and best rational approximation 
Thursday, November 12, 2009 
3:00 pm, ES 146 

Alex Suciu , Northeastern University
Geometry and topology of cohomology jumping loci 
Friday, December 4, 2009 
3:00 pm, ES 143



Spring 2009

Alfonso Montes Rodriguez, University of Sevilla
Heisenberg's Uncertainity Principle and Uniqueness Sets for the Klein-Gordon Equation 
Wednesday, February 4, 2009
3:00 pm, ES 143 

Boo Rim Choe, Korea University, Seoul
Finite Rank Toeplitz Products 
Wednesday, February 25, 2009
4:00 pm, ES 147 

Hyungwoon Koo, Korea University, Seoul
Composition Operator in Several Variables 
Friday, February 27, 2009
4:00 pm, ES 143 

Yum-Tong Siu, Harvard University
A New Interface Between Analysis and Algebraic Geometry 
Friday, April 24, 2009
3:00 pm, ES 143 

Adrian Vasiu, Binghamton University
Reconstructing p-Divisible Groups from Their Truncations of Small Level 
Friday, May 1, 2009
3:00 pm, ES 143 



Fall 2008

Bruce Berndt , University of Illinios, Urbana-Champaign
Ramanujan's Lost Notebook 
Friday, October 3, 2008, at 3:00 p.m. 

Vadim Kozlov, Moscow State University
Mathematical Aspects of the Simplex-Code Approach to Recognition of the Images 
Friday, October 17, 2008, at 3:00 p.m. 

Kehe Zhu, University at Albany
The Mathematics of Boris Korenblum-past, present, and future 
Friday, November 21, 2008, at 3:00 p.m. 

Liming Ge, Chinese Academy of Sciences and University of New Hampshire
Kadison-Singer Algebras 
Friday, December 5, 2008
3:00 pm, ES 143



Spring 2008

John McCarthy, Washington University
Extending bounded analytic functions 
Wednesday, January 16, 2008, at 3:00 p.m. (note unusual time!)

Zhong-Jin Ruan , University of Illinios, Urbana-Champaign
Operator Spaces and Their Applications to Operator Algebras 
Thursday, March 20, 2008, at 4:15 p.m. (note unusual time!)



Fall 2007

Kurt Luoto, University of Washington
A matroid-friendly basis for quasisymmetric functions
Wednesday, September 12, 2007, at 2:00 p.m. (note unusual time!)
Other formats:
Vitaly Maiorov, Technion, Israel
Geometrical properties of the ridge functions manifold
Friday, September 28, 2007, at 4:15 p.m.
Other formats:
Alberto De Sole, Harvard University
Classical and Quantum W Algebras
Friday, October 26, 2007, at 4:15 p.m.
Other formats:
Vladimir Eiderman, University of Kentucky and Michigan State University
Cartan type estimates for certain vector-valued potentials
Friday, November 30, 2007, at 4:15 p.m.
Other formats:
Pavle Pandzic, Cornell University
Dirac Operators and Unitary Representations
Friday, December 7, 2007, at 4:15 p.m.
Other formats: