Seminars and Colloquia by Series

Time-Reversal and Reciprocity Breaking in Electromechanical Metamaterials and Structural Lattics

Series
GT-MAP Seminar
Time
Friday, April 15, 2016 - 15:00 for 2 hours
Location
Skiles 006
Speaker
Prof. Massimo Ruzzene – Aerospace Engineering and Mechanical Engineering, Georgia Tech –
Recent breakthroughs in condensed matter physics are opening new directions in band engineering and wave manipulation. Specifically, challenging the notions of reciprocity, time-reversal symmetry and sensitivity to defects in wave propagation may disrupt ways in which mechanical and acoustic metamaterials are designed and employed, and may enable totally new functionalities. Non-reciprocity and topologically protected wave propagation will have profound implications on how stimuli and information are transmitted within materials, or how energy can be guided and steered so that its effects may be controlled or mitigated. The seminar will briefly introduce the state-of-the-art in this emerging field, and will present initial investigations on concepts exploiting electro-mechanical coupling and chiral and non-local interactions in mechanical lattices. Shunted piezo-electric patches are exploited to achieve time-modulated mechanical properties which lead to one-directional wave propagation in one-dimensional mechanical waveguides. A framework to realize helical edge states in two identical lattices with interlayer coupling is also presented. The methodology systematically leads to mechanical lattices that exhibit one-way, edge-bound, defect-immune, non-reciprocal wave motion. The presented concepts find potential application in vibration reduction, noise control or stress wave mitigation systems, and as part of surface acoustic wave devices capable of isolator, gyrator and circulator-like functions on compact acoustic platforms.

Long range order in random three-colorings of Z^d

Series
Combinatorics Seminar
Time
Friday, April 15, 2016 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ohad Noy Feldheim – Stanford University

Please Note: Joint work with Yinon Spinka.

Consider a random coloring of a bounded domain in the bipartite graph Z^d with the probability of each color configuration proportional to exp(-beta*N(F)), where beta>0, and N(F) is the number of nearest neighboring pairs colored by the same color. This model of random colorings biased towards being proper, is the antiferromagnetic 3-state Potts model from statistical physics, used to describe magnetic interactions in a spin system. The Kotecky conjecture is that in such a model with d >= 3, Fixing the boundary of a large even domain to take the color $0$ and high enough beta, a sampled coloring would typically exhibits long-range order. In particular a single color occupies most of either the even or odd vertices of the domain. This is in contrast with the situation for small beta, when each bipartition class is equally occupied by the three colors. We give the first rigorous proof of the conjecture for large d. Our result extends previous works of Peled and of Galvin, Kahn, Randall and Sorkin, who treated the zero beta=infinity case, where the coloring is chosen uniformly for all proper three-colorings. In the talk we shell give a glimpse into the combinatorial methods used to tackle the problem. These rely on structural properties of odd-boundary subsets of Z^d. No background in statistical physics will be assumed and all terms will be thoroughly explained.

On some models in classical statistical mechanics

Series
Math Physics Seminar
Time
Friday, April 15, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alex Grigo – The University of Oklahoma –
In this talk we will consider a few different mathematical models of gas-like systems of particles, which interact through binary collisions that conserve momentum and mass. The aim of the talk will be to present how one can employ ideas from dynamical systems theory to derive macroscopic properties of such models.

A Quadratic Relaxation for a Dynamic Knapsack Problem with Stochastic Item Sizes

Series
ACO Student Seminar
Time
Friday, April 15, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel Blado – Georgia Tech
We examine a variant of the knapsack problem in which item sizes are random according to an arbitrary but known distribution. In each iteration, an item size is realized once the decision maker chooses and attempts to insert an item. With the aim of maximizing the expected profit, the process ends when either all items are successfully inserted or a failed insertion occurs. We investigate the strength of a particular dynamic programming based LP bound by examining its gap with the optimal adaptive policy. Our new relaxation is based on a quadratic value function approximation which introduces the notion of diminishing returns by encoding interactions between remaining items. We compare the bound to previous bounds in literature, including the best known pseudopolynomial bound, and contrast their corresponding policies with two natural greedy policies. Our main conclusion is that the quadratic bound is theoretically more efficient than the pseudopolyomial bound yet empirically comparable to it in both value and running time.

Intersection numbers and higher derivatives of L-functions for function fields

Series
Athens-Atlanta Number Theory Seminar
Time
Thursday, April 14, 2016 - 17:15 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zhiwei Yun – Stanford University
In joint work with Wei Zhang, we prove a higher derivative analogue of the Waldspurger formula and the Gross-Zagier formula in the function field setting under the assumption that the relevant objects are everywhere unramified. Our formula relates the self-intersection number of certain cycles on the moduli of Shtukas for GL(2) to higher derivatives of automorphic L-functions for GL(2).

Nonabelian Cohen-Lenstra Heuristics and Function Field Theorems

Series
Athens-Atlanta Number Theory Seminar
Time
Thursday, April 14, 2016 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Melanie Matchett-Wood – University of Wisconsin
The Cohen-Lenstra Heuristics conjecturally give the distribution of class groups of imaginary quadratic fields. Since, by class field theory, the class group is the Galois group of the maximal unramified abelian extension, we can consider the Galois group of the maximal unramified extension as a non-abelian generalization of the class group. We will explain non-abelian analogs of the Cohen-Lenstra heuristics due to Boston, Bush, and Hajir and joint work with Boston proving cases of the non-abelian conjectures in the function field analog.

Introduction to Center Manifold Theory

Series
Dynamical Systems Working Seminar
Time
Thursday, April 14, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 170
Speaker
Jiayin Jin – Georgia Tech
In this talk, I will state the main results of center manifold theory for finite dimensional systems and give some simple examples to illustrate their applications. This is based on the book “Applications of Center Manifold Theory” by J. Carr.

The slicing problems for sections of proportional dimensions

Series
School of Mathematics Colloquium
Time
Thursday, April 14, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Koldobskiy – University of Missouri, Columbia –
We consider the following problem. Does there exist an absolute constant C such that for every natural number n, every integer 1 \leq k \leq n, every origin-symmetric convex body L in R^n, and every measure \mu with non-negative even continuous density in R^n, \mu(L) \leq C^k \max_{H \in Gr_{n-k}} \mu(L \cap H}/|L|^{k/n}, where Gr_{n-k} is the Grassmannian of (n-k)-dimensional subspaces of R^n, and |L| stands for volume? This question is an extension to arbitrary measures (in place of volume) and to sections of arbitrary codimension k of the hyperplace conjecture of Bourgain, a major open problem in convex geometry. We show that the above inequality holds for arbitrary origin-symmetric convex bodies, all k and all \mu with C \sim \sqrt{n}, and with an absolute constant C for some special class of bodies, including unconditional bodies, unit balls of subspaces of L_p, and others. We also prove that for every \lambda \in (0,1) there exists a constant C = C(\lambda) so that the above inequality holds for every natural number, every origin-symmetric convex body L in R^n, every measure \mu with continuous density and the codimension of sections k \geq \lambda n. The latter result is new even in the case of volume. The proofs are based on a stability result for generalized intersections bodies and on estimates of the outer volume ratio distance from an arbitrary convex body to the classes of generalized intersection bodies.

The Kelmans-Seymour conjecture V: no contractible edges or triangles (finding TK_5)

Series
Graph Theory Seminar
Time
Wednesday, April 13, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yan Wang – Math, GT
Let G be a 5-connected nonplanar graph. To show the Kelmans-Seymour conjecture, we keep contracting a connected subgraph on a special vertex z until the following happens: H does not contain K_4^-, and for any subgraph T of H such that z is a vertex in T and T is K_2 or K_3, H/T is not 5-connected. In this talk, we study the structure of these 5-separations and 6-separations, and prove the Kelmans-Seymour conjecture.

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