Seminars Sorted by Series
Mathematical Conversations
Cohomology Theories and Formal Groups
6:00pm|Simons Hall Dilworth Room
In the 1960's, Quillen found a remarkable relationship between a
certain class of cohomology theories and the theory of formal
groups. This discovery has had a profound impact on algebraic
topology. In this talk, I'll give a brief exposition of...
How and Why to Formalize Mathematics
6:00pm|Simons Hall Dilworth Room
After a short crash course in using Lean to formalize
mathematics, we will discuss potential applications to and
implications for mathematics education, publication, and
research.
Fair Duels, Digital Halftoning, and Other Mathematical Bit-Balancing Acts
6:00pm|Simons Hall Dilworth Room
What are some of the ways in which binary-valued functions can
accurately approximate continuous-valued ones? This talk will be a
gentle exposition of the mathematics of "noise-shaping
quantization" presented through motivating applications. We
will...
The Mathematical Storytelling of Sand Drawings.
6:00pm|Simons Hall Dilworth Room
Sand drawings appear in many cultures coming, for instance, from
South India, Oceania, and Africa.
We will focus on the Chowke people who have a beautiful
tradition that combines mathematics and storytelling. In their free
time, they would engage in...
On Stable Commutator Length and its New Relatives
6:00pm|Simons Hall Dilworth Room
Stable commutator length (or scl) of group elements is a
well-known, simple-to-define invariant, related to bounded
cohomology and quasimorphisms. Yet its simple definition is a trap:
many of the exciting developments around scl required
"better"...
Mind Your q’s — Quantum Rules on the Grassmannian
6:00pm|Simons Hall Dilworth Room
The theory of quantum cohomology was developed in the early
1990s by physicists working in the field of superstring theory.
Mathematicians then discovered applications to enumerative
geometry, counting the number of rational curves of a given
degree...
6:00pm|Simons Hall Dilworth Room
Expansion is an important notion in graphs, and comes in several
equivalent formulations, including (1) convergence of random walks,
(2) having no small cuts, and (3) having a large spectral
gap. I will talk about a higher dimensional
generalization...
Aperiodic Square Tilings and Lattices in Products of Trees
6:00pm|Simons Hall Dilworth Room
We will consider finite collections of squares tiles, and ask
when we can tile the whole plane in an interesting way. This
question is related to the algebraic structure of ‘lattices in
products of trees’, which are discrete groups acting...
Visual Aspects of Gaussian Periods
6:00pm|Simons Hall Dilworth Room
Gaussian periods are certain sums of roots of unity. Gauss
introduced them in his work on straight edge and compass
constructions of regular polygons. Since then, Gaussian
periods have played important roles in number theory and
beyond. It turns...
Open Books and Secret Agents
6:00pm|Birch Garden, Simons Hall
An open book is a topological concept aptly named by Elmar
Winkelnkemper.
The binding of the book is a fibred knot (of any dimension), and
open books and fibred knots are essentially synonymous. Currently
the standard reference for the existence and...
The Chromatic Picture of Stable Homotopy Theory
6:00pm|Birch Garden, Simons Hall
There is a deep connection between stable homotopy theory
and the theory of formal groups, first noticed by Quillen. I will
describe this connection, and explain how this has led to the
chromatic picture of the stable homotopy category.
Three Fingers are Enough to Count to N (Or, How Not to Hang a Painting)
6:00pm|Simons Hall Dilworth Room
In this talk, I’ll describe one of the most surprising
algorithms in computer science: a way to count arbitrarily high
while maintaining just three bits of state and a clock. It turns
out that the main idea behind the algorithm also appears in
a...
6:00pm|Simons Hall Dilworth Room
I will talk very briefly about what number theorists call
special values of $zeta$ and L-functions. I will start
with some familiar, classical equalities and will attempt to touch
upon some less familiar (mostly conjectural and very far
reaching)...
Mathematics of the Heart and Spirit: Some Thoughts on Grothendieck
6:00pm|Rubenstein Commons | Meeting Room 5
Alexander Grothendieck was one of the greatest thinkers, and one
of the most unusual personalities, in the history of science.
In addition to some biographical details, this talk will offer a
perspective on his approach to mathematics.
6:00pm|Simons Hall Dilworth Room
I will start with an interesting symmetry of plane
quadrilaterals and see what mathematics we can reach within 20
minutes. Also I will explain the title.
Jordan Ellenberg
6:00pm|Simons Hall Dilworth Room
In a recent collaboration with a group of algebraic
combinatorists at ICERM, we came across a rather surprising set of
permutations, which (in a natural sense I'll explain in the talk)
form an unexpectedly gigantic hypercube. This set of...
6:00pm|Simons Hall Dilworth Room
A Lipschitz velocity field gives a reassuring picture of
particle motion: each starting point traces a single, well-defined
trajectory. But many velocity fields arising in geometry, kinetic
theory, and fluid dynamics are far rougher, and then the...
6:00pm|Simons Hall Dilworth Room
I'll discuss our attempts to model problems of bio molecular
assembly using simple geometric constructions. We contrast how
nature makes polyhedra with classical constructions. The issue that
really bothers me is this: biomolecular codes are...
Symmetry and Regularity in Geometry
6:00pm|Simons Hall Dilworth Room
We will give a hopefully light hearted introduction to the
behavior of some geometrically motivated equations, mostly in the
context of examples and broad discussion of Einstein manifolds
(though our story has counterparts in many areas). A theme...
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Mathematical Physics Seminar
Conformal Invariance and the Diffusion on Moduli Space for Radial SLE
We show that a random simple curve in a planar n-connected
domain that is conformally invariant and satisfies a Markovian-type
property, can be described by a diffusion on a moduli space of
dimension 3n-2. Under a natural symmetry condition...
Matrix Models, Random Partitions, Planar Graphs and Random Surfaces
"We give an overview of the ideas and techniques relating these
seemingly different subjects. I will start from the classical
examples, such as enumeration of triangulations by means of one
matrix model and counting of colored graphs (Ising model on...
Seiberg-Witten Theory and Random Partitions
This will be an overview of the paper hep-th/0306238 written
jointly with N. Nekrasov. Our main idea is the interpretation of
the low-energy effective prepotential of the N=2 supersymmetric
gauge theory as the free energy of a certain natural...
Large Deviations for a Point Process of Bounded Variability
Eugene Speer
A (one-dimensional) translation invariant point process of
bounded variability is one in which the variance of the number of
particles in any interval is bounded, uniformly in the length of
the interval. This represents a strong suppression of...
Jamming and k-core Percolation
Andrea Liu
We have proposed that the glass transition is one example of a
broader class of jamming transitions, where systems can develop
extremely long stress relaxation times in disordered states as
temperature is lowered, an applied shear stress is lowered...
We will discuss this model of a random simple path and its
connection to spanning trees, matrix formulas, the Potts model and
SLE. Time permitting, we shall discuss the proof the it has a
scaling limit in three dimensions. No prior knowledge will
be...
Matrix Models for Random Circular Ensembles
We construct an ensemble of (sparse) random matrices whose
eigenvalues follow the Gibbs distribution for n particles of
Coulomb gas on the unit circle at any given inverse temperature.
Our approach combines elements from the theory of orthogonal...
Universality for Orthogonal and Symplectic Ensembles
Percy Deift
This is joint work with Dimitri Gioev. The speaker will show how
to prove universality in the bulk and at the edge for orthogonal
and symplectic ensembles of random matrices with weights of the
form exp(-V(x))dx. The method follows the formalism of...
Lowest Energy States in Non-Relativistic QED
Within non-relativistic quantum electrodnamics, atoms
interacting with the radiation field are expected to have a ground
state. It is further expected that the ground state exists
independently of the size of the coupling constant $\alpha$ and
the...
Edge and Bulk Currents in 2D Disordered Magnetic Systems
The integer quantum Hall effect (IQHE) entails a very precise
quantization of the Hall conductance in a 2D sample at very low
temperatures. Depending on whether the currents in the sample are
ascribed to the bulk or the edge, two apparently...
Resonances and Formation of the Gaps in the Spectrum of Quasi-Periodic Schrödinger Equation
3:00pm|Fine Hall 314, Princeton University
Ionization in Time Periodic Fields of Arbitrary Strength: The Hydrogen Atom
The Thermodynamics Pressure of a Dilute Fermi Gas
Robert Seiringer
We consider a gas of fermions with non-zero spin at positive
temperature $T$. We show that if the range of the interparticle
interaction is small compared to the mean particle distance, the
thermodynamic pressure differs to leading order from the...
Nonequilibrium Stationary States: An Overview
On the Fourier Law for Coupled Oscillators
Anti Kupiainen
We discuss the problem of deriving Fourier's law of heat
transport in a Hamiltonian system of coupled anharmonic oscillators
subject to boundary noise and derive it in a closure approximation
of the stationary state of the system.
Blow Ups in Complex Solutions of the 3D-Navier-Stokes System and Renormalization Group Method
Yakov Sinai
Droplet Minimizers for Free Energy Functionals with a Liquid-Vapor Transition at the Droplet Formation Threshold
Eric Carlen
We examine several non convex free energy functionals involving
a double well potential, and an energy term that penalizes
variation in the mass density field. The simplest example is the
so--called Cahn--Hilliard functional, which is purely...
Microscopic Models for Thermal Conductivity
Stefano Olla
Directed Polymers with Quenched Randomness: Delocalization Transition and Critical Properties
Fabio Toninelli
I will present results on the critical behavior of directed
polymer models interacting with a defect line, in presence of
quenched disorder. These models show a localization-delocalization
phase transition. Our main result is that the transition in...
Cardy's Formula for Certain Models of the Bond-Triangular Type
Lincoln Chayes
A model based on independent bond percolation is defined. It is
demonstrated that this model exhibits critical behavior and, at
least at the level of Cardy's formula, has the same limiting
continuum behavior as the site model.
On the Connection Between SLE and CFT
Critical 2d Models on the Annulus
John Cardy
I conjecture a form for the scaling limit of the partition
function of the critical O(n) and Potts models on the annulus,
using Coulomb gas methods. This has several subtleties whose
elucidation sheds light on the nature of the Coulomb gas
mapping.
Random band matrices have been proposed as an effective, or toy,
model for a disorder induced localization-delocalization transition
of eigenstates. Most results about these matrices, and the
transition, are based on numerics or on calculations with...
