## Seminars and Colloquia by Series

Monday, December 4, 2017 - 14:00 , Location: Skiles 006 , Soren Galatius , Stanford University , Organizer: Kirsten Wickelgren
The general linear groups GL_n(A) can be defined for any ring A, and Quillen's definition of K-theory of A takes these groups as its starting point.  If A is commutative, one may define symplectic K-theory in a very similar fashion, but starting with the symplectic groups Sp_{2n}(A), the subgroup of GL_{2n}(A) preserving a non-degenerate skew-symmetric bilinear form.  The result is a sequence of groups denoted KSp_i(A) for i = 0, 1, ....  For the ring of integers, there is an interesting action of the absolute Galois group of Q on the groups KSp_i(Z), arising from the moduli space of polarized abelian varieties.  In joint work with T. Feng and A. Venkatesh we study this action, which turns out to be an interesting extension between a trivial representation and a cyclotomic representation.
Friday, December 1, 2017 - 15:00 , Location: Skiles 005 , , MIT , , Organizer: Lutz Warnke
Suppose we want to find the largest independent set or maximal cut in a sparse Erdos-Renyi graph, where the average degree is constant. Many algorithms proceed by way of local decision rules, for instance, the "nibbling" procedure. I will explain a form of local algorithms that captures many of these. I will then explain how these fail to find optimal independent sets or cuts once the average degree of the graph gets large. There are some nice connections to entropy and spin glasses.
Series: Other Talks
Friday, December 1, 2017 - 15:00 , Location: Skiles 171 , Shreyas Casturi, Jonathan Chen, Vignesh Raman, Kyle Xiao , Gatech undergraduates , Organizer: Balazs Strenner
This is a brief (15 minute) presentation of an undergraduate project that took place in the 2017 Fall semester.
Friday, December 1, 2017 - 14:00 , Location: Skiles 006 , Bunimovich, Fathi, Grigoriev, de la Llave and Zeng , GT Math and Physics , Organizer: Sung Ha Kang
Thursday, November 30, 2017 - 15:05 , Location: Skiles 006 , , Duke University , , Organizer: Gerandy Brito
Cars are placed with density p on the lattice. The remaining vertices are parking spots that can fit one car. Cars then drive around at random until finding a parking spot. We study the effect of p on the availability of parking spots and observe some intriguing behavior at criticality. Joint work with Michael Damron, Janko Gravner, Hanbeck Lyu, and David Sivakoff. arXiv id: 1710.10529.
Thursday, November 30, 2017 - 13:30 , Location: Skiles 005 , Shijie Xie , Math, Gt , Organizer: Robin Thomas
Let G be a graph containing 5 different vertices a0, a1, a2, b1 and b2. We say that (G, a0, a1, a2, b1, b2) is feasible if G contains disjoint connected subgraphs G1, G2, such that {a0, a1, a2}⊆V(G1) and {b1, b2}⊆V(G2). In this talk, we will complete a sketch of our arguments for characterizing when (G, a0, a1, a2, b1, b2) is feasible. Joint work with Changong Li, Robin Thomas, and Xingxing Yu.
Thursday, November 30, 2017 - 11:05 , Location: Skiles 006 , , Stanford University , , Organizer: Michael Damron
Random effects models are commonly used to measure genetic variance-covariance matrices of quantitative phenotypic traits. The population eigenvalues of these matrices describe the evolutionary response to selection. However, they may be difficult to estimate from limited samples when the number of traits is large. In this talk, I will present several results describing the eigenvalues of classical MANOVA estimators of these matrices, including dispersion of the bulk eigenvalue distribution, bias and aliasing of large "spike" eigenvalues, and distributional limits of eigenvalues at the spectral edges. I will then discuss a new procedure that uses these results to obtain better estimates of the large population eigenvalues when there are many traits, and a Tracy-Widom test for detecting true principal components in these models. The theoretical results extend proof techniques in random matrix theory and free probability, which I will also briefly describe.This is joint work with Iain Johnstone, Yi Sun, Mark Blows, and Emma Hine.
Wednesday, November 29, 2017 - 13:55 , Location: Skiles 005 , Catherine Beneteau , University of South Florida , Organizer: Shahaf Nitzan
In this talk, I will discuss some polynomials that are best approximants (in some sense!) to reciprocals of functions in some analytic function spaces of the unit disk.  I will examine the extremal problem of finding a zero of minimal modulus, and will show how that extremal problem is related to the spectrum of a certain Jacobi matrix and real orthogonal polynomials on the real line.
Wednesday, November 29, 2017 - 13:55 , Location: Skiles 006 , Anubhav Mukherjee , Georgia Tech , Organizer: Jennifer Hom
I'll try to describe some known facts about 3 manifolds. And in the end I want to give some idea about Geometrization Conjecture/theorem.
Wednesday, November 29, 2017 - 12:10 , Location: Skiles 006 , Chongchun Zeng , Georgia Tech , Organizer:
In this talk, we consider the structure of a real $n \times n$ matrix in the form of $A=JL$, where $J$ is anti-symmetric and $L$ is symmetric. Such a matrix comes from a linear Hamiltonian ODE system with $J$ from the symplectic structure and the Hamiltonian energy given by the quadratic form $\frac 12\langle Lx, x\rangle$. We will discuss the distribution of the eigenvalues of $A$, the relationship between the canonical form of $A$ and the structure of the quadratic form $L$, Pontryagin invariant subspace theorem, etc. Finally, some extension to infinite dimensions will be mentioned.