Talk_id  Date  Speaker  Title 
4111

Thursday 9/7 4:10 PM

MSU Postdocs

Postdoc Lightning Talks
 Postdoc Lightning Talks
 09/07/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 MSU Postdocs
No abstract available.

4113

Friday 9/8 3:00 PM

Robert J. Rietz, MAAA

Actuarial Kickoff Lecture
 Actuarial Kickoff Lecture
 09/08/2017
 3:00 PM  4:30 PM
 B117 Wells Hall
 Robert J. Rietz, MAAA
"Effects of Gainsharing Provisions on the Selection of a
Discount Rate for a Defined Benefit Pension Plan

4091

Thursday 9/14 4:10 PM

Jason Starr, Stony Brook University

Solving polynomials with (higher) positive curvature
 Solving polynomials with (higher) positive curvature
 09/14/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Jason Starr, Stony Brook University
A smooth solution set of a system of complex polynomials is a manifold that can be studied geometrically. About 15 years ago, two results proved the existence of solutions of the system over a "function field of a complex curve" (GraberHarrisStarr) and over a finite field (Esnault) provided the associated complex manifolds have positive curvature in a weak sense (rational connectedness). More recently, when
the manifold satisfies a higher version of positive curvature (rational simple connectedness), a similar result was proved over a function field of a complex surface (de JongHeStarr). I will explain these results, some applications to algebra (Serre's "Conjecture II", "PeriodIndex"), and recent extensions, joint with Chenyang Xu, to "function fields over finite fields" and Ax's "PAC fields".

4106

Thursday 9/28 4:10 PM

Günter Stolz, University of Alabama Birmingham

What is manybody localization?
 What is manybody localization?
 09/28/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Günter Stolz, University of Alabama Birmingham
The phenomenon of manybody localization (MBL), as opposed to oneparticle or Anderson localization, has recently received strong attention in the physics and quantum information literature. We will discuss the difference between these two concepts and then propose disordered quantum spin systems as a suitable model to study MBL. Among the possible manifestations of MBL we will mention the absence of manybody (or information) transport as well as area laws for the quantum entanglement of eigenstates. Examples where these properties can be proven include the random XY chain and, more recently, the droplet regime of the random XXZ chain. But many problems remain open.

4125

Wednesday 10/4 4:10 PM

Demetrios Christodoulou, ETH Zurich

The Development of Shocks in Compressible Fluids
 The Development of Shocks in Compressible Fluids
 10/04/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Demetrios Christodoulou, ETH Zurich
The lecture shall trace the history of the theoretical study of the formation and evolution of shocks in compressible fluids, starting with the fundamental work of Riemann, the first work on nonlinear hyperbolic partial differential equations. Riemann considered the case of plane symmetry where the problem reduces to 1 spatial dimension. One milestone in the development of the theory was the work of Sideris who gave the first general proof of the finite time breakdown of smooth solutions in 3 spatial dimensions. Another milestone was the work of Majda who first addressed the problem of the local in time continuation of a shock front as a nonlinear free boundary problem for a nonlinear hyperbolic system of partial differential equations. I shall then discuss my own work, which uses differential geometric methods and resolves the resulting singularities giving a complete description in terms of smooth functions.
My first work studies the maximal smooth development of given smooth initial data, the boundary of the domain of this development, and the behavior of the solution at this boundary. The boundary contains certain singular hypersurfaces which originate from certain singular surfaces. The singular surfaces do occur in nature, but not the singular hypersurfaces. My second work studies the physical evolution beyond the singular surfaces by solving a nonlinear free boundary problem with singular initial conditions associated to each of the singular surfaces. From each singular surface a shock hypersurface issues which appears as the corresponding free boundary.

4092

Thursday 10/5 4:10 PM

Björn Sandstede, Brown University

Nonlinear stability of sources
 Nonlinear stability of sources
 10/05/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Björn Sandstede, Brown University
Defects are interfaces that mediate between two wave trains with possibly different wave numbers. Of particular interest in applications are sources for which the group velocities of the wave trains to either side of the defect point away from the interface. While sources are ubiquitous in experiments and can be found easily in numerical simulations of appropriate models, their stability analysis still presents many challenges. One difficulty is that sources are not travelling waves but are timeperiodic in an appropriate moving coordinate frame. A second difficulty is that perturbations are transported towards infinity, which makes it difficult to apply various commonly used approaches. In this talk, I will discuss nonlinear stability results for sources in general reactiondiffusion system and outline a proof that utilizes pointwise estimates.

4093

Thursday 10/12 4:10 PM

Frank Sottile, Texas A&M University

Galois groups in Enumerative Geometry and Applications
 Galois groups in Enumerative Geometry and Applications
 10/12/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Frank Sottile, Texas A&M University
In 1870 Jordan explained how Galois theory can be applied
to problems from enumerative geometry, with the group encoding intrinsic structure of the problem. Earlier Hermite showed the equivalence of Galois groups with geometric monodromy groups, and in 1979 Harris initiated the modern study of Galois groups of enumerative problems. He posited that a Galois group should be `as large as possible' in that it will be the largest group preserving internal symmetry in the geometric problem.
I will describe this background and discuss some work
in a longterm project to compute, study, and use Galois
groups of geometric problems, including those that arise
in applications of algebraic geometry. A main focus is
to understand Galois groups in the Schubert calculus, a
wellunderstood class of geometric problems that has long
served as a laboratory for testing new ideas in enumerative
geometry.

4129

Thursday 10/19 4:10 PM

Laura DeMarco, Northwestern University

Complex dynamics and elliptic curves
 Complex dynamics and elliptic curves
 10/19/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Laura DeMarco, Northwestern University
In this talk, I will present some connections between recent research in dynamical systems and the classical theory of elliptic curves and rational points. The main goal is to explain the role of dynamical stability and bifurcations in deducing arithmetic finiteness statements. I will focus on three examples: (1) the theorem of Mordell and Weil from the 1920s, presented from a dynamical point of view; (2) a recent result of Masser and Zannier about torsion points on elliptic curves, and (3) features of the Mandelbrot set.

4094

Thursday 10/26 4:10 PM

Alan Reid, Rice University

Arithmetic of Dehn surgery points and Azumaya algebras
 Arithmetic of Dehn surgery points and Azumaya algebras
 10/26/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Alan Reid, Rice University
Associated to a finite volume hyperbolic 3manifold is a
number field and a quaternion algebra over that number field. Closed hyperbolic 3manifolds arising from Dehn surgeries on a hyperbolic knot complement provide a family of number fields and quaternion algebras that can be viewed as "varying" over a certain curve component (the socalled canonical component) of the SL(2,C)character variety of the knot group. This talk will give examples of different behavior and survey recent work on how the varying behavior can be explained using the language of Azumaya algebras over the canonical curve.

5162

Thursday 11/2 4:10 PM

Mike Hill, UCLA

TBA
 TBA
 11/02/2017
 4:10 PM  5:00 PM
 C304 Wells Hall
 Mike Hill, UCLA
No abstract available.
