Colloquium
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.
Next lecture:
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.
Earlier colloquia and abstracts:
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.
“Mathematics In Literature” — Is That Really A Math Course?
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 http://www.albany.edu/math/coll/
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
groups.
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.
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.
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
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Fall 2009
Wednesday, September 16, 2009 4:15 pm (note unusual time!), ES 147 Friday, October 30, 2009 3:00 pm, ES 143 Thursday, November 12, 2009 3:00 pm, ES 146 Friday, December 4, 2009 3:00 pm, ES 143 |
Spring 2009
Wednesday, February 4, 2009 3:00 pm, ES 143 Wednesday, February 25, 2009 4:00 pm, ES 147 Friday, February 27, 2009 4:00 pm, ES 143 Friday, April 24, 2009 3:00 pm, ES 143 Friday, May 1, 2009 3:00 pm, ES 143 |
Fall 2008
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Spring 2008
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Fall 2007
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Affiliated webs
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Department of Mathematics and Statistics
University at Albany, State University of New York - Earth Science 110 1400 Washington Avenue Albany, NY 12222 PHONE (518) 442-4600 FAX (518) 442-4731
