# Seminars & Events for 2017-2018

##### Taylor Proudman columns: "rotation stabilizes the fluid around the 2D flow..."

##### Quantum Markov Semigroups with detailed balance as gradient flow for relative entropy and entropy production inequalities

Semigroups of completely positive trace preserving maps satisfying a certain detailed balance condition are gradient flow driven by dissipation of the quantum relative entropy with respect to a non-commutative analog of the 2-Wasserstein metric on the space of probability densities on Euclidean space.

##### Transcendence of period maps

Period domains D can be described as certain analytic open sets of flag varieties; due to the presence of monodromy, however, the period map of a family of algebraic varieties lands in a quotient D/\Gamma by an arithmetic group. In the very special case when D/\Gamma is itself algebraic, understanding the interaction between algebraic structures on the source and target of the uniformization D

##### Elliptic curves of rank two and generalised Kato classes

The generalised Kato classes of Darmon-Rotger arise as p-adic limits of diagonal cycles on triple products of modular curves, and in some cases, they are predicted to have a bearing on the arithmetic of elliptic curves over Q of rank two. In this talk, we will report on a joint work in progress with Ming-Lun Hsieh concerning a special case of the conjectures of Darmon-Rotger.

##### TBA - Nicolas Garcia Trillos

##### Singular Volume Problems

We give general results for the asymptotics and anomaly for volumes of regions with respect to measures that are singular along hypersurfaces. These have applications to holography in physical models as well as invariant theory for embedded hypersurfaces. In both cases one solves an appropriate bulk problem with boundary data specified along the singular hypersurface.

##### Positive Mass Conjecture

In this talk, I will talk about the positive mass conjecture, which, roughly speaking, asserts that the total mass of an isolated physical object with positive local energy density must be nonnegative. I will begin with the ADM formalism in general relativity and the history of positive mass (energy) conjecture.

##### An invariance on dynamical systems

In this talk, we mainly discuss limit sets, particularly omega-limit sets and attractors which are invariant on dynamical systems. We first deal with envelope theory related to IFS and its applications. We also discuss the invariant notions on 3-manifolds with a certain cohomology condition.

##### Ekman pumbing: "rotation stabilizes the boundary layer in the inviscid limit..."

##### The stable Cannon Conjecture for torsion-free Farrell-Jones groups

The torsion-free case of a well-known (open!!) conjecture of Cannon says: Let G be a torsion free hyperbolic group.

##### Comparing exponential and Erdős–Rényi random graphs, and a general bound on the distance between Bernoulli random vectors

We present a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of 1) a mixing quantity for the Glauber dynamics of one of the sequences, and 2) a simple expectation of the other.

##### The bipolar filtration of topologically slice knots

The bipolar filtration of Cochran, Harvey and Horn initiated the study of deeper structures of the smooth concordance group of the topologically slice knots. We show that the graded quotient of the bipolar filtration has infinite rank at each stage greater than one.

##### A converse theorem of Gross-Zagier and Kolyvagin: CM case.

Let E be a CM elliptic curves over rationals and p an odd prime ordinary for E. If the Z_p corank of p^\infty Selmer group for E equals one, then we show that the analytic rank of E also equals one.

This is joint work with Ashay Burungale.

##### Self-similar structure of caustics and shock formation

Caustics are places where the light intensity diverges, and where the wave front has a singularity. We use a self-similar description to derive the detailed spatial structure of a cusp singularity, from where caustic lines originate. We use this insight to study shock formation in the dKP equation, as well as shocks in classical compressible Euler dynamics.

##### TBA-Laura Starkston

##### Nonlinear descent on moduli of local systems

In 1880, Markoff studied a cubic Diophantine equation in three variables now known as the Markoff equation, and observed that its integral solutions satisfy a form of nonlinear descent.

##### Packing the discrete torus

Let H be an induced subgraph of the toroidal grid Z_k^m and suppose that

|V(H)| divides some power of k. We show that if k is even then (for

large m) the torus has a perfect vertex-packing with induced copies of H.

##### Packing the discrete torus

Let H be an induced subgraph of the toroidal grid Z_k^m and suppose that

| V(H)| divides some power of k. We show that if k is even then (for

large m) the torus has a perfect vertex-packing with induced copies of H.

##### An equivariant Quillen theorem

The canonical map from the \Z/2-equivariant Lazard ring, defined by Cole-Greenlees-Kriz, to the \Z/2-equivariant

homotopy theoretic complex bordism ring, defined by tom Dieck, is an isomorphism. Joint work with Michael Wiemeler

##### On the notion of genus for division algebras and algebraic groups.

Let D be a central division algebra of degree n over a field K. One defines the genus gen(D) of D as the set of classes [D'] in the Brauer group Br(K) where D' is a central division K-algebra of degree n having the same isomorphism classes of maximal subfields as D.