[math-ias] Mathematics Seminars -- Week of September 30, 2013

[Anthony V. Pulido]

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540

Mathematics Seminars
Week of September 30, 2013




Monday, September 30

Computer Science/Discrete Mathematics Seminar I
Topic:         Some provable bounds for deep learning
Speaker:     Sanjeev Arora
Time/Room:     11:15am - 12:15pm/S-101
Abstract:    See below

Short talks by postdoctoral members
Topic:         The Newton stratification of Shimura varieties
Speaker:     Arno Kret, University of Paris XI; Member, School of
Mathematics
Time/Room:     2:00pm - 2:15pm/S-101

Topic:         G-valued flat deformations and local models
Speaker:     Brandon Levin, Stanford University; Member, School of
Mathematics
Time/Room:     2:15pm - 2:30pm/S-101

Topic:         Branching laws for representations of real reductive groups
Speaker:     Yoshiki Oshima, University of Tokyo; Member, School of
Mathematics
Time/Room:     2:30pm - 2:45pm/S-101

Topic:         Interactive Channel Capacity
Speaker:     Gillat Kol, Weizmann Institute of Science; Member, School of
Mathematics
Time/Room:     4:00pm - 4:15pm/S-101

Topic:         Cylindrical contact homology as a well-defined homology?
Speaker:     Joanna Nelson, University of Wisconsin-Madison
Time/Room:     4:15pm - 4:30pm/S-101

Topic:         Depth complexity and communication games
Speaker:     Or Meir, Institute for Advanced Study; Member, School of
Mathematics
Time/Room:     4:30pm - 4:45pm/S-101



Tuesday, October 1

Computer Science/Discrete Mathematics Seminar II
Topic:         Small set expander flows
Speaker:     Ali Kemal Sinop, Institute for Advanced Study; Member, School
of Mathematics
Time/Room:     10:30am - 12:30pm/S-101
Abstract:    See below

Short talks by postdoctoral members
Topic:         On Rearrangements of Fourier Series
Speaker:     Mark Lewko, University of California, Los Angeles; Member,
School of Mathematics
Time/Room:     2:00pm - 2:15pm/S-101

Topic:         Log-integrability of Rademacher Fourier series, with
applications to random analytic functions
Speaker:     Alon Nishry, Tel Aviv University; Member, School of Mathematics
Time/Room:     2:15pm - 2:30pm/S-101

Topic:         High Dimensional Expanders
Speaker:     Ori Parzanchevski, Hebrew University of Jerusalem; Member,
School of Mathematics
Time/Room:     2:30pm - 2:45pm/S-101

Topic:         Fundamental groups of singular varieties
Speaker:     Bhargav Bhatt, Institute for Advanced Study; Member, School of
Mathematics
Time/Room:     2:45pm - 3:00pm/S-101

Topic:         Diffusion in high Sobolev spaces for Hamiltonian PDEs
Speaker:     Oana Pocovnicu, Princeton University; Member, School of
Mathematics
Time/Room:     4:00pm - 4:15pm/S-101

Topic:         Value distribution of long Dirichlet polynomials and
applications to the Riemann zeta-function
Speaker:     Maksym Radziwill, Stanford University; Member, School of
Mathematics
Time/Room:     4:15pm - 4:30pm/S-101

Topic:         Continued fractions in general relativity
Speaker:     Michael Reiterer, ETH Zurich; Member, School of Mathematics
Time/Room:     4:30pm - 4:45pm/S-101



Wednesday, October 2

Workshop on Topology: Identifying Order in Complex Systems
Topic:         Tracing medieval Migration through Next Generation
Sequencing: Finding Meaningful Models in a Sea of Data
Speaker:     Patrick J. Geary, Institute for Advanced Study; Faculty,
School of Historical Studies
Time/Room:     2:00pm - 3:00pm/S-101

IAS/Princeton University Wednesday Seminar on Perfectoid Spaces
Speaker:     To Be Announced
Time/Room:     2:00pm - 4:00pm/Fine 322, Princeton University

Workshop on Topology: Identifying Order in Complex Systems
Topic:         The Topology of Viral Evolution
Speaker:     Raúl Rabadán, Columbia University
Time/Room:     3:30pm - 4:30pm/S-101

Mathematical Conversations
Speaker:     To Be Announced
Time/Room:     6:00pm - 7:30pm/Dilworth Room



Thursday, October 3

Working Group on Algebraic Number Theory
Speaker:     To Be Announced
Time/Room:     2:00pm - 4:00pm/Fine 214, Princeton University

Joint IAS/Princeton University Number Theory Seminar
Topic:         Pairs of p-adic L-functions for elliptic curves at
supersingular primes
Speaker:     Florian Sprung, Princeton University; Member, School of
Mathematics
Time/Room:     4:30pm - 5:30pm/Fine 214, Princeton University
Abstract:    See below



Friday, October 4

Princeton/IAS Symplectic Geometry Seminar
Topic:         Positive loops and orderability in contact geometry
Speaker:     Peter Weigel, Purdue University
Time/Room:     1:00pm - 2:00pm/S-101
Abstract:    See below

Short talks by postdoctoral members
Topic:         Homotopy Type Theory: what can logic do for homotopy theory?
Speaker:     Peter Lumsdaine, Institute for Advanced Study; Member, School
of Mathematics
Time/Room:     2:00pm - 2:15pm/S-101

Topic:         Exponential-time algorithms for NP problems: prospects and
limits
Speaker:     Andrew Drucker, Institute for Advanced Study; Member, School
of Mathematics
Time/Room:     2:15pm - 2:30pm/S-101

Topic:         Computational aspects of the Combinatorial Nullstellensatz
method via a polynomial approach to matrix and hypermatrix algebra
Speaker:     Edinah Gnang, Rutgers, The State University of New Jersey;
Member, School of Mathematics
Time/Room:     2:30pm - 2:45pm/S-101

Topic:         Approximability of graph partitioning problems
Speaker:     Ali Sinop, Institute for Advanced Study; Member, School of
Mathematics
Time/Room:     2:45pm - 3:00pm/S-101

Topic:         p-adic versions of BSD
Speaker:     Florian Sprung, Brown University; Member, School of Mathematics
Time/Room:     4:00pm - 4:15pm/S-101

Topic:         Determining algebraic subgroups from invariant dimensions
Speaker:     Jun Yu, Institute for Advanced Study; Member, School of
Mathematics
Time/Room:     4:15pm - 4:30pm/S-101

Topic:         Scissors Congruence and K-theory
Speaker:     Inna Zakharevich, Massachusetts Institute of Technology;
Member, School of Mathematics
Time/Room:     4:30pm - 4:45pm/S-101

1 Some provable bounds for deep learning
   Sanjeev Arora

Deep learning, a modern version of neural nets, is increasingly seen as a
promising way to implement AI tasks such as speech recognition and image
recognition. Most current algorithms are heuristic and have no provable
guarantees. This talk will describe provable learning of an interesting
class of deep networks which are neural nets. Here a deep net is viewed as
a generative model for a probability distribution on inputs, using the
"denoising autoencoder" framework of Vincent et al. The talk will be
self-contained. (Joint work with Aditya Bhaskara, Rong Ge, Tengyu Ma)

2 Small set expander flows
   Ali Kemal Sinop

A common way for lower bounding the expansion of a graph is by looking the
second smallest eigenvalue of its Laplacian matrix. Also known as the easy
direction of Cheeger's inequality, this bound becomes too weak when the
expansion is o(1). In 2004, Arora, Rao and Vazirani proved the existence of
"expander flows", which are certificates of graph expansion up to a factor
of O(sqrt{log n}). In this talk, I will describe a generalization of these
for small set, "small set expander (SSE) flows", and I will describe an
application of such flows for finding near optimal sparse cuts on graphs
with certain isoperimetric profiles. This is joint work with Sanjeev Arora
and Rong Ge.

3 Pairs of p-adic L-functions for elliptic curves at supersingular primes
   Florian Sprung

Iwasawa Theory for elliptic curves/modular forms has been traditionally in
better shape at ordinary primes than at supersingular ones. After sketching
the ordinary theory, we will indicate what makes the supersingular case
more complicated, and then introduce *pairs* of objects that that are as
simple as their ordinary counterparts. These pairs of objects work in
tandem to shed some light on the nature of ranks of elliptic curves and the
size of Sha along cyclotomic Z_p extensions.

4 Positive loops and orderability in contact geometry
   Peter Weigel

Orderability of contact manifolds is related in some non-obvious ways to
the topology of a contact manifold $\Sigma$. We know, for instance, that if
$\Sigma$ admits a 2-subcritical Stein filling, it must be non-orderable. By
way of contrast, in this talk I will discuss ways of modifying Liouville
structures for high-dimensional $\Sigma$ so that the result is always
orderable. The main technical tool is a Morse-Bott Floer theoretic growth
rate, which has some parallels with Givental's nonlinear Maslov index. I
will also discuss a generalization to the relative case, and applications
to bi-invariant metrics on $Cont(\Sigma)$.

IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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