[iasmath-semru] Mathematics Seminars--Week of December 10, 2018

Fri Dec 7 17:06:49 EST 2018

INSTITUTE FOR ADVANCED STUDY

School of Mathematics

Princeton, NJ 08540

Mathematics Seminars

Week of December 10, 2018

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To view mathematics in titles and abstracts, please click on the talk's
link.

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Monday, December 10

Computer Science/Discrete Mathematics Seminar I

Topic:                    A matrix expander Chernoff bound

Speaker:              Ankit Garg, Microsoft Research

Time/Room:       11:15am - 12:15pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=128879>
http://www.math.ias.edu/seminars/abstract?event=128879

Seminar on Theoretical Machine Learning

Topic:                    On Expressiveness and Optimization in Deep
Learning

Speaker:              Nadav Cohen, Member, School of Mathematics

Time/Room:       12:15pm - 1:45pm/White Levy Room

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=139466>
http://www.math.ias.edu/seminars/abstract?event=139466

Members' Seminar

Topic:                    Schubert polynomials via triangulations of flow
polytopes

Speaker:              Karola Meszaros, Cornell University; von Neumann
Fellow, School of Mathematics

Time/Room:       2:00pm - 3:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=129398>
http://www.math.ias.edu/seminars/abstract?event=129398

Symplectic Dynamics/Geometry Seminar

Topic:                    Upper bounds on the Lagrangian spectral norm

Speaker:              Egor Shelukhin, University of Montreal

Time/Room:       3:30pm - 5:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=137931>
http://www.math.ias.edu/seminars/abstract?event=137931

Tuesday, December 11

Computer Science/Discrete Mathematics Seminar II

Topic:                    An invitation to tensor networks

Speaker:              Michael Walter, University of Amsterdam

Time/Room:       10:30am - 12:30pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=129115>
http://www.math.ias.edu/seminars/abstract?event=129115

Variational Methods in Geometry Seminar

Topic:                    Density and equidistribution of minimal
hypersurfaces

Speaker:              Andre Neves, University of Chicago; Member, School of
Mathematics

Time/Room:       1:00pm - 3:00pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=140489>
http://www.math.ias.edu/seminars/abstract?event=140489

Symplectic Dynamics Working Group

Topic:                    Hamiltonian pseudo-rotations of projective spaces.

Speaker:              Zhengyi Zhou, Member, School of Mathematics

Time/Room:       1:30pm - 3:00pm/Simonyi Hall Classroom 114

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=140627>
http://www.math.ias.edu/seminars/abstract?event=140627

Variational Methods in Geometry Seminar

Topic:                    Harmonic maps into singular spaces

Speaker:              Brian Freidin, Brown University; Visitor, School of
Mathematics

Time/Room:       3:30pm - 5:30pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=138893>
http://www.math.ias.edu/seminars/abstract?event=138893

Wednesday, December 12

Informal Group Action Seminar

Speaker:              Ilya Khayutin, Princeton University; Veblen Research
Instructor, School of Mathematics

Time/Room:       2:00pm - 3:15pm/Simonyi Hall 101

Mathematical Conversations

Topic:                    How to detect a projective space?

Speaker:              Jakub Witaszek, Member, School of Mathematics

Time/Room:       6:00pm - 7:30pm/Dilworth Room

Thursday, December 13

Venkatesh Working Group

Time/Room:       10:00am - 12:00pm/Simonyi Hall 101

Working Seminar in Algebraic Number Theory

Time/Room:       2:00pm - 4:00pm/Fine Hall 1201

Joint IAS/Princeton University Number Theory Seminar

Topic:                    Nearby cycles over general bases and duality

Speaker:              Weizhe Zheng, Morningside Center of Mathematics
(Chinese Academy of Sciences)

Time/Room:       4:30pm - 5:30pm/Fine Hall 214

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=139873>
http://www.math.ias.edu/seminars/abstract?event=139873

Friday, December 14

Allen-Cahn/Ginzburg-Landau Reading group

Time/Room:       10:00am - 12:00pm/Simonyi Hall 101

Analysis Seminar

Topic:                    TBD

Speaker:              Eugenia Malinnikova, NTNU; von Neumann Fellow, School
of Mathematics

Time/Room:       4:30pm - 5:30pm/Simonyi Hall 101

1 A matrix expander Chernoff bound 
   Ankit Garg 

Chernoff-type bounds study concentration of sums of independent random
variables and are extremely useful in various settings. In many settings,
the random variables may not be completely independent but only have limited
independence. One such setting, which turns out to be useful in
derandomization and theoretical computer science, in general, involves
random walks on expanders. I will talk about a Chernoff-type bound for sums
of matrix-valued random variables sampled via a random walk on an expander.
Our proof is based on a new multi-matrix extension of the Golden-Thompson
inequality which improves in some ways a recent inequality due to Sutter et
al. and may be of independent interest, as well as an adaptation of an
argument for the scalar case due to Healy. Based on joint work with Yin Tat
Lee, Zhao Song and Nikhil Srivastava.

http://www.math.ias.edu/seminars/abstract?event=128879

2 On Expressiveness and Optimization in Deep Learning 
   Nadav Cohen 

Understanding deep learning calls for addressing three fundamental
questions: expressiveness, optimization and generalization. Expressiveness
refers to the ability of compactly sized deep neural networks to represent
functions capable of solving real-world problems. Optimization concerns the
effectiveness of simple gradient-based algorithms in solving non-convex
neural network training programs. Generalization treats the phenomenon of
deep learning models not overfitting despite having much more parameters
than examples to learn from. This talk will describe a series of works aimed
at unraveling some of the mysteries behind expressiveness and optimization.
I will begin by establishing an equivalence between convolutional and
recurrent networks --- the most successful deep learning architectures to
date --- and hierarchical tensor decompositions. The equivalence will be
used to answer various questions concerning expressiveness, resulting in new
theoretically-backed tools for deep network design. I will then turn to
discuss a recent line of work analyzing optimization of deep linear neural
networks. By studying the trajectories of gradient descent, we will derive
the most general guarantee to date for efficient convergence to global
minimum of a gradient-based algorithm training a deep network. Moreover, in
stark contrast with conventional wisdom, we will see that sometimes,
gradient descent can train a deep linear network faster than a classic
linear model. In other words, depth can accelerate optimization, even
without any gain in expressiveness, and despite introducing non-convexity to
a formerly convex problem. 

The talk will be of a high-level nature, suitable for a diverse crowd. It
will cover works done in collaboration with Sanjeev Arora, Noah Golowich,
Elad Hazan, Wei Hu, Yoav Levine, Or Sharir, Amnon Shashua, Ronen Tamari and
David Yakira.

http://www.math.ias.edu/seminars/abstract?event=139466

3 Schubert polynomials via triangulations of flow polytopes 
   Karola Meszaros 

The flow polytope associated to an acyclic graph is the set of all
nonnegative flows on the edges of the graph with a fixed netflow at each
vertex. We will discuss a family of subdivisions of flow polytopes and
explain how they give rise to a family of Schubert polynomials, which
generalize the well known basis of the ring of symmetric functions, Schur
polynomials. We will also show that the Newton polytopes of Schubert
polynomials are generalized permutahedra; the latter were (re)introduced by
Postnikov in 2005. We explain the connections between generalized
permutahedra and flow polytopes, thereby tying all our main players
together.. 

Based on joint work with Laura Escobar, Alex Fink and Avery St. Dizier.

http://www.math.ias.edu/seminars/abstract?event=129398

4 Upper bounds on the Lagrangian spectral norm 
   Egor Shelukhin 

We discuss recent developments in establishing uniform bounds on the
spectral norm and related invariants in the absolute and relative settings.
In particular, we describe new progress on a conjecture of Viterbo asserting
such bounds for exact deformations of the zero section in unit cotangent
disk bundles. This talk is partially based on joint work with Asaf Kislev.

http://www.math.ias.edu/seminars/abstract?event=137931

5 An invitation to tensor networks 
   Michael Walter 

Tensor networks describe high-dimensional tensors as the contraction of a
network (or graph) of low-dimensional tensors. Many interesting tensor can
be succinctly represented in this fashion -- from many-body ground states in
quantum physics to the matrix multiplication tensors in algebraic
complexity. I will give a mathematical introduction to the formalism, give
several examples, and sketch some of the most important results. We will
discuss the role of the network, how symmetries are encoded, tensor networks
as a computational model, and survey some recent algorithmic results.

http://www.math.ias.edu/seminars/abstract?event=129115

6 Density and equidistribution of minimal hypersurfaces 
   Andre Neves 

I will outline the proof of density of minimal hypersurfaces
(Irie-Marques-Neves) and equidistribution of minimal hypersurfaces
(Marques-Neves-Song).

http://www.math.ias.edu/seminars/abstract?event=140489

7 Hamiltonian pseudo-rotations of projective spaces. 
   Zhengyi Zhou 

I will talk about Ginzburg and Gurel's work on Hamiltonian pseudo-rotations
of projective spaces, in particular, their proof of no fixed point of a
pseudo-rotation of projective space is isolated as an invariant set.

http://www.math.ias.edu/seminars/abstract?event=140627

8 Harmonic maps into singular spaces 
   Brian Freidin 

In the 90's, Gromov and Schoen introduced the theory of harmonic maps into
singular spaces, in particular Euclidean buildings, in order to understand
p-adic superrigidity. The study was quickly generalized in a number of
directions by a number of authors. This talk will focus on the work
initiated by Korevaar and Schoen on harmonic maps into metric spaces with
curvature bounded above in the sense of Alexandrov. I will describe the
variational characterization of harmonic maps into such spaces, some
analytic consequences, and in particular a Bochner formula capturing the
role of both the domain and target curvatures

http://www.math.ias.edu/seminars/abstract?event=138893

9 Nearby cycles over general bases and duality 
   Weizhe Zheng 

Over one-dimensional bases, Gabber and Beilinson proved theorems on the
commutation of the nearby cycle functor and the vanishing cycle functor with
duality. In this talk, I will explain a way to unify the two theorems,
confirming a prediction of Deligne. I will also discuss the case of
higher-dimensional bases and applications to local acyclicity, following
suggestions of Illusie and Gabber. This is joint work with Qing Lu.

http://www.math.ias.edu/seminars/abstract?event=139873

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

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