Seminars and Colloquia by Series

Simplifying curves on surfaces (undergraduate project)

Series
Other Talks
Time
Friday, December 1, 2017 - 15:00 for 30 minutes
Location
Skiles 171
Speaker
Shreyas Casturi, Jonathan Chen, Vignesh Raman, Kyle Xiao – Gatech undergraduates
This is a brief (15 minute) presentation of an undergraduate project that took place in the 2017 Fall semester.

Sub-optimality of local algorithms for some problems on sparse random graphs

Series
Combinatorics Seminar
Time
Friday, December 1, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mustazee Rahman – MIT –
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.

Parking

Series
Stochastics Seminar
Time
Thursday, November 30, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Matthew Junge – Duke University –
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.

Two-three linked graphs

Series
Graph Theory Seminar
Time
Thursday, November 30, 2017 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shijie Xie – Math, Gt
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.

Eigenvalues in multivariate random effects models

Series
Job Candidate Talk
Time
Thursday, November 30, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zhou Fan – Stanford University –
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.

Survey on 3-manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, November 29, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav Mukherjee – Georgia Tech
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.

Zeros of optimal polynomial approximants and spectra of Jacobi matrices

Series
Analysis Seminar
Time
Wednesday, November 29, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Catherine Beneteau – University of South Florida
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.

Linear algebra of Hamiltonian matrices

Series
Research Horizons Seminar
Time
Wednesday, November 29, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chongchun Zeng – Georgia Tech
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.

Geometric tangential methods in nonlinear diffusive PDE

Series
PDE Seminar
Time
Tuesday, November 28, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Eduardo Teixeira – University of Central Florida –
Geometric tangential analysis refers to a constructive systematic approach based on the concept that a problem which enjoys greater regularity can be “tangentially" accessed by certain classes of PDEs. By means of iterative arguments, the method then imports regularity, properly corrected through the path used to access the tangential equation, to the original class. The roots of this idea likely go back to the foundation of De Giorgi’s geometric measure theory of minimal surfaces, and accordingly, it is present in the development of the contemporary theory of free boundary problems. This set of ideas also plays a decisive role in Caffarelli’s work on fully non-linear elliptic PDEs, and subsequently in his studies on Monge-Ampere equations from the 1990’s. In recent years, however, geometric tangential methods have been significantly enhanced, amplifying their range of applications and providing a more user-friendly platform for advancing these endeavors. In this talk, I will discuss some fundamental ideas supporting (modern) geometric tangential methods and will exemplify their power through select examples.

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