Seminars and Colloquia Schedule

Mining mesoscale physics from polycrystalline data sets

Series
CDSNS Colloquium
Time
Monday, November 2, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Siddharth Maddali – Carnegie Mellon
I present a formalism and an computational scheme to quantify the dynamics of grain boundary migration in polycrystalline materials, applicable to three-dimensional microstructure data obtained from non-destructive coarsening experiments. I will describe a geometric technique of interface tracking using well-established optimization algorithms and demonstrate how, when coupled with very basic physical assumptions, one can effectively measure grain boundary energy density and mobility of a given misorientation type in the two-parameter subspace of boundary inclinations. By doing away with any specific model or parameterization for the energetics, I seek to have my analysis applicable to general anisotropies in energy and mobility. I present results in two proof-of-concept test cases, one first described in closed form by J. von Neumann more than half a century ago, and the other which assumes analytic but anisotropic energy and mobility known in advance.

Applications of number theory in hyperbolic geometry

Series
Geometry Topology Seminar
Time
Monday, November 2, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
BoGwang Jeon – Columbia University –
In this talk, first, I'll briefly go over my proof of the conjecture that there are only afinite number of hyperbolic 3-manifolds of bounded volume and trace field degree. Then I'lldiscuss some conjectural pictures to quantitative results and applications to other similarproblems.

Co-dimension One Motion and Assembly

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 2, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor James von Brecht – Cal State University, Long Beach
In this talk, I will discuss mathematical models and tools for analyzing physical and biological processes that exhibit co-dimension one characteristics. Examples include the assembly of inorganic polyoxometalate (POM) macroions into hollow spherical structures and the assembly of surfactant molecules into micelles and vesicles. I will characterize when such structures can arise in the context of isotropic and anisotropic models, as well as applications of these insights to physical models of these behaviors.

Rational curves on elliptic surfaces

Series
Algebra Seminar
Time
Monday, November 2, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Doug Ulmer – Georgia Tech
Given a non-isotrivial elliptic curve E over K=Fq(t), there is always a finite extension L of K which is itself a rational function field such that E(L) has large rank. The situation is completely different over complex function fields: For "most" E over K=C(t), the rank E(L) is zero for any rational function field L=C(u). The yoga that suggests this theorem leads to other remarkable statements about rational curves on surfaces generalizing a conjecture of Lang.

The de Rham fundamental group, continued

Series
Nonabelian Chabauty Seminar
Time
Monday, November 2, 2015 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Douglas Ulmer – Georgia Tech
I will finish my overview of the de Rham fundamental group by reviewing two explicit calculations: Deligne's completely concrete description of the unipotent fundamental group of the projective line minus three points in terms of the free nilpotent Lie algebra on two generators, and Chen's general calculation of the unipotent fundamental group of a manifold in terms of iterated integrals.

Polynomials and (Finite) Free Probability

Series
ACO Seminar
Time
Tuesday, November 3, 2015 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Adam Marcus – Mathematics and PACM, Princeton University
Recent work of the speaker with Dan Spielman and Nikhil Srivastava introduced the ``method of interlacing polynomials'' (MOIP) for solving problems in combinatorial linear algebra. The goal of this talk is to provide insight into the inner workings of the MOIP by introducing a new theory that reveals an intimate connection between the use of polynomials in the manner of the MOIP and free probability, a theory developed by Dan Voiculescu as a tool in the study of von Neumann algebras. I will start with a brief introduction to free probability (for those, like me, who are not operator theorists). In particular, I will discuss the two basic operations in free probability theory (the free additive and free multiplicative convolutions), and how they relate to the asymptotic eigenvalue distributions of random matrices. I will then show how certain binary operations on polynomials act as finite analogues of the free convolutions and how the MOIP is effectively transferring the asymptotic bounds obtained in free probability to bounds in the new theory (which can then be applied to finite scenarios). If time permits, I will show how such a theory gives far better intuition as to how one might apply the MOIP in the future, using recent results on restricted invertibility and the existence of Ramanujan graphs as examples.

Weak Galerkin Finite Element Methods for PDEs

Series
Research Horizons Seminar
Time
Wednesday, November 4, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chunmei Wang – Department of Mathematics, Georgia Institute of Technology –

Food and Drinks will be provided before the seminar.

Weak Galerkin (WG) is a new finite element method for partial differential equations where the differential operators (e.g., gradient, divergence, curl, Laplacian etc) in the variational forms are approximated by weak forms as generalized distributions. The WG discretization procedure often involves the solution of inexpensive problems defined locally on each element. The solution from the local problems can be regarded as a reconstruction of the corresponding differential operators. The fundamental difference between the weak Galerkin finite element method and other existing methods is the use of weak functions and weak derivatives (i.e., locally reconstructed differential operators) in the design of numerical schemes based on existing variational forms for the underlying PDE problems. Weak Galerkin is, therefore, a natural extension of the conforming Galerkin finite element method. Due to its great structural flexibility, the weak Galerkin finite element method is well suited to most partial differential equations by providing the needed stability and accuracy in approximation. In this talk, the speaker will introduce a general framework for WG methods by using the second order elliptic problem as an example. Furthermore, the speaker will present WG finite element methods for several model PDEs, including the linear elasticity problem, a fourth order problem arising from fluorescence tomography, and the second order problem in nondivergence form. The talk should be accessible to graduate students with adequate training in computational mathematics.

Math Problems in Gene Regulation

Series
School of Mathematics Colloquium
Time
Thursday, November 5, 2015 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Caroline Uhler – MIT –
Although the genetic information in each cell within an organism is identical, gene expression varies widely between different cell types. The quest to understand this phenomenon has led to many interesting mathematics problems. First, I will present a new method for learning gene regulatory networks. It overcomes the limitations of existing algorithms for learning directed graphs and is based on algebraic, geometric and combinatorial arguments. Second, I will analyze the hypothesis that the differential gene expression is related to the spatial organization of chromosomes. I will describe a bi-level optimization formulation to find minimal overlap configurations of ellipsoids and model chromosome arrangements. Analyzing the resulting ellipsoid configurations has important implications for the reprogramming of cells during development. Any knowledge of biology which is needed for the talk will be introduced during the lecture.

More on Logarithmic sums of convex bodies

Series
Stochastics Seminar
Time
Thursday, November 5, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christos Saraoglou – Kent State University
We prove that the log-Brunn-Minkowski inequality (log-BMI) for the Lebesgue measure in dimension n would imply the log-BMI and, therefore, the B-conjecture for any even log-concave measure in dimension n. As a consequence, we prove the log-BMI and the B-conjecture for any even log-concave measure, in the plane. Moreover, we prove that the log-BMI reduces to the following: For each dimension n, there is a density f_n, which satisfies an integrability assumption, so that the log-BMI holds for parallelepipeds with parallel facets, for the density f_n. As byproduct of our methods, we study possible log-concavity of the function t -> |(K+_p\cdot e^tL)^{\circ}|, where p\geq 1 and K, L are symmetric convex bodies, which we are able to prove in some instances and as a further application, we confirm the variance conjecture in a special class of convex bodies. Finally, we establish a non-trivial dual form of the log-BMI.

Ergodic Measures for shifts with eventually constant complexity growth

Series
CDSNS Colloquium
Time
Friday, November 6, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jon Fickenscher – Princeton University –
We will consider (sub)shifts with complexity such that the difference from n to n+1 is constant for all large n. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most d/2 ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss further improvements when more assumptions are allowed. This is ongoing work with Michael Damron.

Folkman Numbers

Series
ACO Student Seminar
Time
Friday, November 6, 2015 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Troy Retter – Emory University
For an integer k, the Folkman number f(k) is the least integer n for which there exists a graph G on n vertices that does not contain a clique of size k and has the property that every two coloring of E(G) yields a monochromatic clique of size of size k. That is, it is the least number of vertices in a K_{k+1}-free graph that is Ramsey to K_k. A recent result of Rodl, Rucinski, and Schacht gives an upper bound on the Folkman numbers f(k) which is exponential in k. A fundamental tool in their proof is a theorem of Saxton and Thomason on hypergraph containers. This talk will give a brief history of the Folkman numbers, introduce the hypergraph container theorem, and sketch the proof of the Rodl, Rucinski, and Schacht result. Recent work with Hiep Han, Vojtech Rodl, and Mathias Schacht on two related problems concerning cycles in graphs and arithmetic progressions in subset of the integers will also be presented.

Analytic methods in graph theory

Series
Joint School of Mathematics and ACO Colloquium
Time
Friday, November 6, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel Kral – University of Warwick

Refreshments will be served in the atrium after the talk.

The theory of combinatorial limits provides analytic ways of representing large discrete objects. The theory has opened new links between analysis, combinatorics, computer science, group theory and probability theory. In this talk, we will focus on limits of dense graphs and their applications in extremal combinatorics. We will present a general framework for constructing graph limits corresponding to solutions of extremal graph theory problems, which led to constructing counterexamples to several conjectures concerning graph limits. At the end, we will discuss limits of sparse graphs and possible directions to unify the existing approaches related to dense and sparse graphs.