# Seminars & Events for 2016-2017

##### Conway mutation and knot Floer homology

Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita-Terasaka and Conway pair.

##### Heat Rises: 100 Years of Rayleigh-Bénard Convection

**Please note 5:30 start time. **Buoyancy forces result from density variations, often due to temperature variations, in the presence of gravity. Buoyancy-driven fluid flows shape the weather, ocean and atmosphere dynamics, the climate, and the structure of the earth and stars.

##### Optics and optimization

We will consider the following airplane boarding policy which was recently implemented by a few airlines: "Passengers with no overhead bin luggage board before those with such luggage". The reasoning for the policy was explained by the CEO of one of the companies as follows.

##### Monotone Lagrangians in cotangent bundles

We show that there is a 1-parameter family of monotone Lagrangian tori in the cotangent bundle of the 3-sphere with the following property: every compact orientable monotone Lagrangian with non-trivial Floer cohomology is not Hamiltonian-displaceable from either the zero-section or one of the tori in the family.

##### Length and Width of Lagrangian Cobordisms

In this talk, I will discuss two measurements of Lagrangian cobordisms between Legendrian submanifolds in symplectizations: their length and their relative Gromov width. The Gromov width, in particular, is a fundamental global invariant of symplectic manifolds, and a relative version of that width helps understand the geometry of Lagrangian submanifolds of a symplectic manifold.

##### Compactification of strata of abelian differentials

Many questions about Riemann surfaces are related to study their flat structures induced from abelian differentials. Loci of abelian differentials with prescribed type of zeros form a natural stratification. The geometry of these strata has interesting properties and applications to moduli of complex curves.

##### Detecting geometric structure in random graphs

We study the problem of detecting the presence of an underlying high-dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erdos-Renyi random graph.

##### On fractional analogues of k-Hessian operators

**Geometric Analysis Learning Seminar:** We consider k-Hessian operators(and when k=n, it is the Monge Amp\’{e}re operator) as convex envelopes of linear operators.

##### Universality of transport coefficients in the Haldane-Hubbard model

**Please note special day (Wednesday), but usual room and time. **In this talk I will review some selected aspects of the theory of interacting electrons on the honeycomb lattice, with special emphasis on the Haldane-Hubbard model: this is a model for interacting electrons on the hexagonal lattice, in the presence of nearest and next-to-nearest neighbor hopping, as well as of a tra

##### State-Of-The Art Machine Learning Algorithms and How They Are Affected By Near-Term Technology Trends

Industry and Wall Street projections indicate that Machine Learning will touch every piece of data in the data center by 2020. This has created a technology arms race and algorithmic competition as IBM, NVIDIA, Intel, and ARM strive to dominate the retooling of the computer industry to support ubiquitous machine learning workloads over the next 3-4 years.

##### Singular points of complex surfaces and Heegaard-Floer homology

I will describe some basic constructions of Singularity Theory and their relation with Low Dimensional Topology. In particular, in the second part of the talk, I want to discuss some relations between complex surface singularities and Heegaard Floer homology.

##### Ergodic measures for a class of subshifts

We will consider minimal subshifts with complexity such that the difference from n to n+1 is constant for all large n and impose one more condition (which we call the Regular Bispecial Condition). The shifts that arise naturally from interval exchange transformations belong to this class. A minimal interval exchange transformation on d intervals has at most d/2 ergodic probability measures.

##### Assessing significance in a Markov chain without mixing

We will describe a new statistical test to demonstrate outlier status for a state of any reversible Markov Chain. Remarkably, the test can rigorously demonstrate outlier status without any bounds on the mixing time of the chain. With an eye on November 8, we will describe an application of our test to representative democracy. This is joint work with Maria Chikina and Alan Frieze.

##### Zeroes of harmonic functions and Laplace eigenfunctions: pursuing the conjectures by Yau and Nadirashvili

**Please note special date - THURSDAY, OCTOBER 13. **Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions.

##### Local points of supersingular elliptic curves on Z_p-extensions

Work of Kobayashi and Iovita-Pollack describes how local points of supersingular elliptic curves on ramified Z_p-extensions of Q_p split into two strands of even and odd points. We will discuss a generalization of this result to Z_p-extensions that are localizations of anticyclotomic Z_p-extensions over which the elliptic curve has non-trivial CM points.

##### The Boltzmann equation with specular boundary condition in convex domains

We establish the global-wellposedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external potential. In particular, we have completely solved the long standing open problem after an announcement of Shizuta and Asano in 1977.

##### Quantum analogues of geometric inequalities for Information Theory

** Please note special day (Monday), time (2:30) and location (Jadwin 303). **Geometric inequalities, such as entropy power inequality or the isoperimetric inequality, relate geometric quantities, such as volumes and surface areas.

##### Testing Distribution Properties

Given samples from an unknown distribution p, is it possible to distinguish whether p belongs to some class of distributions C versus p being far from every distribution in C by some margin? This fundamental question has received extensive study in Statistics, Computer Science and several other fields.

##### From Lusternik-Schnirelmann theory to Conley conjecture

In this talk I will discuss a recent result showing that whenever a closed symplectic manifold admits a Hamiltonian diffeomorphism with finitely many simple periodic orbits, the manifold has a spherical homology class of degree two with positive symplectic area and positive integral of the first Chern class.

##### Convexity in divisor theory

For toric varieties there is a dictionary relating the geometry of divisors to the theory of polytopes. I will discuss how certain aspects of this dictionary can be extended to divisors on arbitrary smooth projective varieties. These results build upon ideas of Khovanskii and Teissier; as in their work, geometric inequalities and convexity theory play an important role.