Seminars Sorted by Series
Members’ Seminar
Spectra of metric graphs and crystalline measures
The geometric optics trace formula gives the singular support of
wave trace on a compact Riemannian manifold. In the case of of a
one dimensional singular manifold, that is a metric (or quantum)
graph, this formula is exact and yields a crystalline...
Direct and dual Information Bottleneck frameworks for Deep Learning
Tali Tishby
The Information Bottleneck (IB) is an information theoretic
framework for optimal representation learning. It stems from the
problem of finding minimal sufficient statistics in supervised
learning, but has insightful implications for Deep Learning...
Lower Bounds in Complexity Theory, Communication Complexity, and Sunflowers
In this talk I will discuss the Sunflower Lemma and similar
lemmas that prove (in various contexts) that a set/distribution can
be partitioned into a structured part and a "random-looking" part.
I will introduce communication complexity as a key...
Towards a mathematical model of the brain
Striving to make contact with mathematics and to be consistent
with neuroanatomy at the same time, I propose an idealized picture
of the cerebral cortex consisting of a hierarchical network of
brain regions each further subdivided into...
The Palais-Smale Theorem and the Solution of Hilbert’s 23 Problem
2:00pm|http://theias.zoom.us/j/119412864
Hilbert’s 23rd Problem is the last in his famous list of
problems and is of a different character than the others. The
description is several pages, and basically says that the calculus
of variations is a subject which needs development. We will...
How to diagonalize a functor
2:00pm|Simonyi Hall 101 and Remote Access
Diagonalization is incredibly important in every field of
mathematics. I am a representation theorist, so I will start by
motivating the uses of diagonalization in representation theory.
Then comes a brief introduction to categorical
representation...
Stability, non-approximated groups and high-dimensional expanders
2:00pm|Simonyi Hall 101 and Remote Access
Several well-known open questions, such as: "are all groups
sofic or hyperlinear?", have a common form: can all groups be
approximated by asymptotic homomorphisms into the symmetric groups
$Sym(n)$ (in the sofic case) or the unitary groups $U(n)$...
Log-concavity, matroids and expanders
2:00pm|Simonyi Hall 101 and Remote Access
Matroids are combinatorial objects that model various types of
independence. They appear several fields mathematics, including
graph theory, combinatorial optimization, and algebraic geometry.
In this talk, I will introduce the theory of matroids...
2:00pm|Simonyi Hall 101 and Remote Access
You can make a paper Moebius band by starting with a $1$ by $L$
rectangle, giving it a twist, and then gluing the ends together.
The question is: How short can you make $L$ and still succeed in
making the thing? This question goes back to B. Halpern...
Metric embeddings, uniform rectifiability, and the Sparsest Cut problem
2:00pm|Simonyi Hall 101 and Remote Access
(joint work with Assaf Naor) A key problem in metric geometry
asks: given metric spaces $X$ and $Y$, how well does $X$ embed in
$Y$? In this talk, we will consider this problem for the case of
the Heisenberg group and explain its connections to...
Some analogies between arithmetic and topology
2:00pm|Simonyi Hall 101 and Remote Access
There are striking analogies between topology and arithmetic
algebraic geometry, which studies the behavior of solutions to
polynomial equations in arithmetic rings. One expression of these
analogies is through the theory of etale cohomology, which...
2:00pm|Simonyi Hall 101 and Remote Access
Growth, isoperimetry and Liouville property for random walks on groups
2:00pm|Simonyi Hall 101 and Remote Access
In a joint work with Tianyi Zheng we show that the growth
function of the first Grigorchuk group satisfies \[ \ln \ln v_n/\ln
v_n = a, \] where $a = \log 2/\log x$, $x$ being a positive root of
the polynomial $x^3-x^2-2x-4$. This is done by...
Support Varieties for Modular Representations
2:00pm|Simonyi Hall 101 and Remote Access
We present an overview of elementary methods to study extensions
of modular representations of various types of "groups". We shall
begin by discussing actions of an elementary abelian $p$-group, $E
= (Z/p)^r$, on finite dimensional vector spaces...
NP-hard problems naturally arising in knot theory
2:00pm|Simonyi Hall 101 and Remote Access
Low-dimensional topology and geometry have many problems with an
easy formulation, but a hard solution. Despite our intuitive
feeling that these problems are "hard", lower or upper bounds on
algorithmic complexity are known only for some of them...
A Feynman Approach to Dynamic Rate Markov Processes
2:00pm|Simonyi Hall 101 and Remote Access
Physics inspired mathematics helps us understand the random
evolution of Markov processes. For example, the Kolmogorov forward
and backward differential equations that govern the dynamics of
Markov transition probabilities are analogous to the...
2:00pm|Simonyi Hall 101 and Remote Access
2:00pm|Simonyi Hall 101 and Remote Access
A nonabelian Brunn-Minkowski inequality
2:00pm|Simonyi Hall 101 and Remote Access
The celebrated Brunn-Minkowski inequality states that for
compact subsets $X$ and $Y$ of $\Bbb{R}^d$, $m(X+Y)^{1/d} \geq
m(X)^{1/d}+m(Y)^{1/d}$ where $m(\cdot)$ is the Lebesgue measure. We
will introduce a conjecture generalizing this inequality to...
The top-heavy conjecture for vectors and matroids
2:00pm|Simonyi Hall 101 and Remote Access
A 1948 theorem of de Bruijn and Erdős says that if $n$ points in
a projective plane do not lie all on a line, then they determine at
least n lines. More generally, Dowling and Wilson conjectured in
1974 that for any finite set of vectors spanning a...
No seminar: Presidents' Day
2:00pm|Simonyi Hall 101 and Remote Access
Astrophysical fluid dynamics
2:00pm|Simonyi Hall 101 and Remote Access
Most of the visible matter in the Universe is a plasma, that is
a dilute gas of ions, electrons, and neutral atoms. In many
circumstances, the dynamics of this plasma can be modeled in the
continuum limit, using the equations of fluid mechanics...
The Value of Errors in Proofs
2:00pm|Simonyi Hall 101 and Remote Access
A few months ago, a group of theoretical computer scientists
posted a paper on the Arxiv with the strange-looking title "MIP* =
RE", impacting and surprising not only complexity theory but also
some areas of math and physics. Specifically, it...
Higher Representation Theory
2:00pm|Simonyi Hall 101 and Remote Access
New types of symmetries have been considered in algebra and
algebraic geometry and a higher analog of representation theory has
been developed to answer questions of classical representation
theory. Geometric representation theory can be viewed as...
Estimating the mean of a real valued distribution
2:00pm|Simonyi Hall 101 and Remote Access
I revisit the basic statistical problem of estimating the mean
of a real-valued distribution. I will introduce an estimator with
the guarantee that "our estimator, on *any* distribution, is as
accurate as the sample mean is for the Gaussian...
Milnor Conjecture Learning Seminar
1:00pm|Rubenstein Commons, Room #5
10:00am|Rubenstein Commons, Room#5
The Beilinson-Lichtenbaum Conjecture
1:00pm|Rubenstein Commons, Room#5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|West Bldg. Lecture Hall
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
1:00pm|Rubenstein Commons | Meeting Room 5
Minerva Distinguished Visitor Lectures at Princeton University
I: Geometry and dynamics on hyperbolic surfaces
4:30pm|McDonnell A02, Princeton University
The first lecture will give some background on the geometry and
dynamics on hyperbolic surfaces. I will give a brief overview of
Teichmüller theory and properties of the mapping class groups and
the space of geodesic currents. I will discuss some...
II: Dynamics on moduli spaces of hyperbolic surfaces
4:30pm|McDonnell A02, Princeton University
In the second lecture, I will discuss several natural geometric
flows defined on bundles over the moduli spaces of curves. I will
describe basic ergodic properties of these flows. I will discuss
some open questions and some of the progress made in...
III: Counting mapping class group orbits on hyperbolic surfaces
4:30pm|McDonnell A02, Princeton University
Let $X$ be a complete hyperbolic metric on a surface of genus
$g$ with $n$ punctures. In this lecture I will discuss the problem
of the growth of $s^{k}_{X}(L)$, the number of closed curves of
length at most $L$ on $X$ with at most $k$ self...
Minerva Mini-Course
An overview of Benjamini-Schramm convergence in group theory and dynamics
Lewis Bowen
1:30pm|Fine 110, Princeton University
Finite models of infinite groups/actions/manifolds are useful
for studying spectral and $L^2$-invariants, constructing random
processes and have recently been used to introduce new invariants
of group actions useful for proving nonembedding and...
$L^2$ invariants and Benjamini-Schramm convergence
Lewis Bowen
1:30pm|Fine 110, Princeton University
Finite models of infinite groups/actions/manifolds are useful
for studying spectral and $L^2$-invariants, constructing random
processes and have recently been used to introduce new invariants
of group actions useful for proving nonembedding and...
When does injectivity imply surjectivity?
Lewis Bowen
1:30pm|Fine 110, Princeton University
Finite models of infinite groups/actions/manifolds are useful
for studying spectral and $L^2$-invariants, constructing random
processes and have recently been used to introduce new invariants
of group actions useful for proving nonembedding and...
Classification of Bernoulli shifts
Lewis Bowen
4:30pm|Fine 314, Princeton University
Finite models of infinite groups/actions/manifolds are useful
for studying spectral and $L^2$-invariants, constructing random
processes and have recently been used to introduce new invariants
of group actions useful for proving nonembedding and...
