| |
|
APRIL 2008 |
| |
|
| Automorphic Forms and Galois Representations |
| Topic: |
Counting Automorphic Forms |
| Presenter: |
Frank Calegari, Northwestern University |
| Date: |
Wednesday, April 16, 2008, Time: 1:30 p.m., Location: Fine Hall 314 |
| Abstract: |
In this talk, I shall present a method for producing new upper bounds for the dimension of certain cohomology groups of arithmetic quotients of symmetric spaces. Suitably interpreted, these results give new upper bounds for spaces of automorphic forms of cohomological type. After explaining why non-trivial lower bounds are (in general) impossible to obtain, I will discuss how p-adically completed spaces of torsion classes can conjecturally be used as a substitute for classical automorphic forms in order to produce large families of Galois representations. This is joint work with Matthew Emerton. |
| |
|
| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
Covers of elliptic curves and the moduli space of curves |
| Presenter: |
D. Chen, Harvard University |
| Date: |
Wednesday, April 16, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Consider genus g curves that admit degree d covers to elliptic curves only branched at one point with a fixed ramification type. The locus of such covers forms a one parameter family Y that naturally maps into the moduli space of genus g curves \bar{M}_g. We study the geometry of Y, and produce a combinatorial method by which to investigate its slope, irreducible components and genus. The results can be used to study the lower bound for slopes of effective divisors on \bar{M}_g. |
| |
|
| Department Colloquium |
| Topic: |
Characters of finite Chevalley groups and categorification |
| Presenter: |
Roma Bezrukavnikov, MIT and IAS |
| Date: |
Wednesday, April 16, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
An important branch of representation theory studies representations of reductive groups over finite fields, such as GL(n,F_q), Sp(2n,F_q) etc. A deep theory due mostly to Lusztig and Shoji provides a classification of irreducible representations and a formula for their characters in terms of certain algebro-geometric objects called character sheaves. In a joint work with M. Finkelberg and V. Ostrik we establish some new nice features of the geometric objects, motivated by an attempt to find a conceptual explanation for the beautiful but somewhat mysterious results of Lusztig and Shoji. |
| |
|
| Graduate Student Seminar |
| Topic: |
Matriod Theory |
| Presenter: |
Melody Chan, Princeton University |
| Date: |
Thursday, April 17, 2008, Time: 12:30 p.m., Location: Fine Hall 214 |
| Abstract: |
Every maximal acyclic subgraph of a given graph has the same number of edges. Every maximal independent subset of a given set of vectors in $\mathbb{R}^n$ has the same size. The common generalization of these lies in matroid theory, which, roughly speaking, is an abstraction of the notion of linear independence. Despite the fact that matroids "forget" quite a lot of structure, they are immensely useful to graph theorists. In this talk, I'll give an introduction to the theory of matroids and point to some of its highlights, keeping graph theory in mind as our primary motivation and source of examples. |
| |
|
| Discrete Mathematics Seminar |
| Topic: |
The Finite Field Kakeya Problem |
| Presenter: |
Xander Faber, Columbia University |
| Date: |
Thursday, April 17, 2008, Time: 2:15 p.m., Location: Fine Hall 314 |
| Abstract: |
If V is a vector space over the field with q elements, a (finite field) Kakeya set is a subset of V containing a line in every direction. The main problem is to determine how large such a set is forced to be. Recently, Zeev Dvir gave a simple proof of the correct order of magnitude of Kakeya sets by introducing a nice technique from algebraic geometry. This new idea has provided a great deal of excitement. In this talk, I'll survey what is known about the problem (relatively little given that it is 10 years old), and then discuss some of the low-hanging combinatorial fruit in the case where V has dimension 2. |
| |
|
| Mathematical Physics Seminar ***Please note special date and time |
| Topic: |
Nontrivial coupling at quantum graph vertices obtained through squeezing of Dirichlet networks |
| Presenter: |
P. Exner, Doppler Inst., Prague |
| Date: |
Thursday, April 17, 2008, Time: 3:15 p.m., Location: Jadwin 343 |
| Abstract: |
The problem discussed in this talk is motivated by efforts to understand approximation of quantum graph Hamiltonians by Laplacians on families of "fat graphs". The emphasis is on new results in the Dirichlet case, however, first we review the background and explain the importance of vertex boundary conditions using a lattice graph example, and mention known result in both the Neumann and Dirichlet setting. After that we suggest a way how a wider classes of vertex couplings can be obtained from squeezed Dirichlet networks. To illustrate the proposed strategy we work out the simplest nontrivial example, a family of bent tubes giving a graph of one vertex and two edges, or a two-parameter family of generalized point interactions on the line. |
| |
|
| Princeton University/Institute for Advanced Study Joint Number Theory Seminar |
| Topic: |
Nonvanishing mod p of Eisenstein series |
| Presenter: |
Bei Zhang, IAS |
| Date: |
Thursday, April 17, 2008, Time: 4:30 p.m., Location: IAS SH-101 |
| |
|
| Topology Seminar |
| Topic: |
Loop products and closed geodesics |
| Presenter: |
Nancy Hingston, College of New Jersey |
| Date: |
Thursday, April 17, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The critical points of the energy function on the free loop space L(M) of a compact Riemannian manifold M are the closed geodesics on M. Filtration by the length function gives a link between the geometry of closed geodesics and the algebraic structure given by the Chas-Sullivan product on the homology of L(M). Geometry reveals the existence of a related product on the cohomology of L(M). For manifolds such as spheres and projective spaces for which there is a metric with all geodesics closed, the resulting homology and cohomology rings are nontrivial, and closely linked to the geometry. I will not assume any knowledge of the Chas-Sullivan product. Joint work with Mark Goresky. |
| |
|
| Symplectic Geometry Seminar |
| Topic: |
Numerical Methods in Calabi-Yau Compactications of String Theory |
| Presenter: |
Sergio Lukic, Rutgers University |
| Date: |
Friday, April 18, 2008, Time: 2:00 p.m., Location: Fine Hall 314 |
| Abstract: |
After a brief introduction to N=1 compatifications in String Theory, it will become clear why one needs to know explicit solutions to important PDEs, such as the Kaehler-Einstein metrics. This fact motivates the use of numerical methods to approximate solutions to such PDEs. Instead of using relaxation methods/finite differences I will explain how to use geometric quantization combined with many powerful results in complex analysis (Yau's theorem, DUY, balanced metrics...) to approximate transcendental objects by algebraic-geometric ones. I will finish by showing several examples of these techniques. |
| |
|
| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Hamiltonian formulation of general relativity and quasilocal mass |
| Presenter: |
Mu-Tao Wang, Columbia University |
| Date: |
Friday, April 18, 2008, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Isometric embeddings of surfaces into the Minkowski space are used as references to derive a quasilocal mass expression from the Hamiltonian formulation of Einstein's equation. This involves an existence and uniqueness theorem of isometric embeddings and a canonical choice of time gauges. We also prove the quasilocal mass is positive under the dominant energy condition and is zero for surfaces in the Minkowski space. This talk is based on joint work with Shing-Tung Yau at Harvard. |
| |
|
| Differential Geometry and Geometric Analysis Seminar ***Please note special time |
| Topic: |
Optimal curvature decays on asymptotically locally Euclidean manifolds |
| Presenter: |
Sophie Chen, Berkeley |
| Date: |
Friday, April 18, 2008, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: |
We present a method to study curvature decays on asymptotically locally Euclidean manifolds. The method is flexible and can also be applied to elliptic systems of reaction-diffusion type. |
| |
|
| Group Actions Seminar |
| Topic: |
Two examples of nonhomogeneous orbit closures |
| Presenter: |
Francois Maucourant, Rennes 1 University |
| Date: |
Monday, April 21, 2008, Time: 12:15 p.m., Location: Fine Hall 224 |
| Abstract: |
We will explain how to construct orbits of non-homogeneous closure for some subgroup of the diagonal group acting on the space of lattices of dimension at least 6. Also, a similar example for the action of *2,*3 on the four dimensionnal torus is discussed. |
| |
|
| Analysis Seminar |
| Topic: |
On singularity formation for certain geometric wave equations |
| Presenter: |
Joachim Krieger, University of Pennsylvania |
| Date: |
Monday, April 21, 2008, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
We dicuss recent results, obtained jointly with W. Schlag and D. Tataru, on a new kind of singularity formation for certain critical nonlinear geometric wave equations. |
| |
|
| Algebraic Geometry Seminar |
| Topic: |
Grothendieck duality via the homotopy category of flat modules |
| Presenter: |
Amnon Neeman, Australian National University |
| Date: |
Tuesday, April 22, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
We will discuss a novel perspective of dualizing complexes which has been discovered in the last three years. We will review three recent articles, by Jorgensen, Krause and Iyengar-Krause, before coming to recent work by myself and by Murfet. |
| |
|
| Mathematical Physics Seminar |
| Topic: |
Long range order for lattice dipoles |
| Presenter: |
Alessandro Giuliani, University of Rome |
| Date: |
Tuesday, April 22, 2008, Time: 4:30 p.m., Location: Jadwin 343 |
| Abstract: |
We consider a system of classical Heisenberg spins on a cubic lattice in dimensions three or more, interacting via the dipole-dipole interaction. We prove that at low enough temperature the system displays orientational long range order, as expected by spin wave theory. The proof is based on reflection positivity methods. In particular, we demonstrate a previously unproven conjecture on the dispersion relation of the spin waves, first proposed by Froehlich and Spencer, which allows one to apply infrared bounds for estimating the long distance behavior of the spin-spin correlation functions. |
| |
|
| Operations Research and Financial Engineering Colloquium |
| Topic: |
Stochastic programming, progressive hedging, and projective splitting methods |
| Presenter: |
Jonathan Eckstein, Rutgers University |
| Date: |
Tuesday, April 22, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
See http://orfe.princeton.edu/papers/eckstein-abstract.pdf |
| |
|
| Princeton University/Institute for Advanced Study Joint Number Theory Seminar ***Please note special date, time, and location |
| Topic: |
Automorphic lifts of prescribed type |
| Presenter: |
Toby Gee, Imperial College and Northwestern |
| Date: |
Wednesday, April 23, 2008, Time: 1:30 p.m., Location: Fine Hall 314 |
| |
|
| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
Equivariant Gromov-Witten theory of orbifold curves |
| Presenter: |
P. Johnson, University of Michigan |
| Date: |
Wednesday, April 23, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Consider a P^1 with effective orbifold structure at 0 and infinity. We show that that the equivariant Gromov-Witten theory of such an orbifold is governed by the 2-Toda hierarchy. The proof follows that of Okounkov and Pandharipande for the case of a smooth P^1, and goes through Hurwitz numbers and the representation theory of the symmetric group. In the case of an ineffective orbifold, the Gromov-Witten theory is governed by commuting copies of the 2-Toda hierarchy, and the symmetric group is replaced by wreath products. |
| |
|
| Department Colloquium |
| Topic: |
TBA |
| Presenter: |
Jim Bryan, UBC |
| Date: |
Wednesday, April 23, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| |
|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Giovanni Forni, University of Maryland |
| Date: |
Thursday, April 24, 2008, Time: 2:00 p.m., Location: Fine Hall 401 |
| |
|
| Discrete Mathematics Seminar |
| Topic: |
An Elegant and Insightful Direct Combinatorial Proof of the Arithmetical Identity 4+5=2+7 |
| Presenter: |
Doron Zeilberger, Rutgers University |
| Date: |
Thursday, April 24, 2008, Time: 2:15 p.m., Location: Fine Hall 110 |
| Abstract: |
There are no trivial theorems, only trivial mathematicians (those who believe that there exist trivial theorems). Being a non-trivial mathematician myself, I will present a new, elegant, and very insightful direct combinatorial proof of the seemingly (to most people) "trivial" arithmetical theorem that states that four plus five equals two plus seven. More important, the methodology should extend to give insightful direct combinatorial proofs of even deeper identities, like (4+6+200+6+50)+(3+10+30+5)=300+4+10. |
| |
|
| Princeton University/Institute for Advanced Study Joint Number Theory Seminar |
| Topic: |
Explicit reduction modulo p of certain crystalline representations |
| Presenter: |
Toby Gee, Imperial College and Northwestern |
| Date: |
Thursday, April 24, 2008, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
We use the p-adic local Langlands correspondence for GL_2(Q_p) to explicitly compute the reduction modulo p of crystalline representations of small slope, and give applications to modular forms. Joint with Kevin Buzzard. |
| |
|
| Symplectic Geometry Seminar |
| Topic: |
Algebraic properties of quantum homology |
| Presenter: |
Yaron Ostrover, MIT |
| Date: |
Friday, April 25, 2008, Time: 2:00 p.m., Location: Fine Hall 314 |
| Abstract: |
In this talk we discuss certain algebraic properties of the quantum homology algebra of toric Fano manifolds. In particular, we describe an easily-verified sufficient condition for the semi-simplicity of the quantum homology. Moreover, we provide some examples of monotone toric Fano manifolds for which the quantum homology is not semi-simple. (This is a joint work with Ilya Tyomkin.) |
| |
|
| Discrete Mathematics Seminar ***Please note special date and location |
| Topic: |
An Elegant and Insightful Direct Combinatorial Proof of the Arithmetical Identity 4+5=2+7 |
| Presenter: |
Doron Zeilberger, Rutgers University |
| Date: |
Friday, April 25, 2008, Time: 2:15 p.m., Location: Fine Hall 110 |
| Abstract: |
There are no trivial theorems, only trivial mathematicians (those who believe that there exist trivial theorems). Being a non-trivial mathematician myself, I will present a new, elegant, and very insightful direct combinatorial proof of the seemingly (to most people) "trivial" arithmetical theorem that states that four plus five equals two plus seven. More important, the methodology should extend to give insightful direct combinatorial proofs of even deeper identities, like (4+6+200+6+50)+(3+10+30+5)=300+4+10. |
| |
|
| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Knots and Topological Growth Laws in the Faddeev Model |
| Presenter: |
Yisong Yang, Poly. Tech. in New York |
| Date: |
Friday, April 25, 2008, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
In this talk, I present some joint work with Fanghua Lin on the existence of knotted solitons realized as the energy-minimizing configurations in the Faddeev field-theoretical model and the associated universal topological growth laws which relate the knot energy to knot topological charge defined by the Hopf invariant. |
| |
|
| Group Actions Seminar |
| Topic: |
TBA |
| Presenter: |
Alex Furman, University of Illinois at Chicago |
| Date: |
Monday, April 28, 2008, Time: 12:15 p.m., Location: Fine Hall 224 |
| |
|
| PACM Colloquium |
| Topic: |
Active and Semi-Supervised Learning Theory |
| Presenter: |
Rob Nowak, Electrical and Computer Engineering, University of Wisconsin-Madison |
| Date: |
Monday, April 28, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Science is arguably the pinnacle of human intellectual achievement, yet the scientific discovery process itself remains an art. Human intuition and experience is still the driving force of the high-level discovery process: we determine which hypotheses and theories to entertain, which experiments to conduct, how data should be interpreted, when hypotheses should be abandoned, and so on. Meanwhile machines are limited to low-level tasks such as gathering and processing data. A grand challenge for scientific discovery in the 21st century is to devise machines that directly participate in the high-level discovery process. Towards this grand challenge, we must formally characterize the limits of machine learning. Statistical learning theory is usually based on supervised training, wherein a learning algorithm is presented with a finite set of i.i.d. labeled training examples. However, modern experimental methods often generate incredibly large numbers of unlabeled data for very little expense, while the task of labeling data is often painstaking and costly. Machine learning methods must leverage the abundance of unlabeled data in scientific problem domains. Active learning (AL) and semi-supervised learing (SSL) are two well known approaches to exploit unlabeled data. In both paradigms one has access to a large pool of unlabeled examples, and only a few labeled examples are provided or selected. AL is a sequential feedback process. Unlabeled examples that are predicted to have very informative labels, based on previously gathered labeled and unlabeled data, are selected for labeling. In SSL, labeled examples are randomly provided, without regard to potential informativeness. Today, little is known about theoretical limits of AL and SSL performance. Sparsity and complexity of the underlying data-generating distributions appear to play a central role in the performance of AL and SSL, and this talk will discuss some of the known theoretical results.
This work is joint with Rui Castro, Aarti Singh and Jerry Zhu. |
| |
|
| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Brendan Hassett, Rice University |
| Date: |
Tuesday, April 29, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
| |
|
| Operations Research and Financial Engineering Colloquium |
| Topic: |
TBA |
| Presenter: |
Farid AitSahlia, University of Florida |
| Date: |
Tuesday, April 29, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| |
|
| Department Colloquium |
| Topic: |
Paint-by-numbers: pattern formation in two-dimensional sheets of cells |
| Presenter: |
Stanislav Shvartsman, Princeton University |
| Date: |
Wednesday, April 30, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
One of the basic mechanisms responsible for the formation of three-dimensional organs relies on the regulated folding of epithelia (two-dimensional sheets of cells). This process is driven by the spatially nonuniform and dynamic distribution of multiple chemical components (products of gene expression) across the epithelia that prepare for folding. Some of the key questions in this class of biological problems are related to the total number of involved genes, the diversity and dynamics of their expression patterns, and the mechanisms of pattern formation. I will present the results of our experimental and computational work that explores these questions during the formation of an elaborate three-dimensional structure (the fruit fly eggshell). I will also try to discuss the mathematical problems associated with the combinatorial construction of complex two-dimensional patterns from a small number of building blocks and dynamics of piecewise linear models of epithelial patter ning. |
| |
|
| Operations Research and Financial Engineering Colloquium |
| Topic: |
Behavioral Portfolio Choice in Continuous Time |
| Presenter: |
Xunyu Zhou, University of Oxford |
| Date: |
Wednesday, April 30, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
See http://orfe.princeton.edu/papers/zhou-abstract.pdf |
| |
|
MAY 2008 |
| |
|
| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Maria Chudnovsky, Columbia University and CMI |
| Date: |
Thursday, May 1, 2008, Time: 2:15 p.m., Location: Fine Hall 314 |
| |
|
| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Robert Lipshitz, Columbia University |
| Date: |
Thursday, May 1, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| |
|
| Operations Research and Financial Engineering Colloquium |
| Topic: |
Game Options, Risk and their Binomial Approximations |
| Presenter: |
Yuri Kifer, Hebrew University |
| Date: |
Monday, May 5, 2008, Time: 3:30 p.m., Location: Friends Bowl 004 |
| Abstract: |
See http://orfe.princeton.edu/papers/kifer-abstract.pdf |
| |
|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Nonconvergence examples in averaging |
| Presenter: |
Yuri Kifer, Hebrew University |
| Date: |
Wednesday, May 7, 2008, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
See http://www.math.princeton.edu/~seminar/2007-08-sem/Kifer2008.pdf |
| |
|
| Operations Research and Financial Engineering Colloquium |
| Topic: |
Competition, Human Capital, and Growth: a MFG stylized model |
| Presenter: |
Jean Michel Lasry |
| Date: |
Thursday, May 8, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| |
|
| Operations Research and Financial Engineering Colloquium |
| Topic: |
TBA |
| Presenter: |
Paulo Silva, University of Sao Paulo |
| Date: |
Thursday, May 15, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| |
|
| |
|