## Seminars and Colloquia by Series

Wednesday, October 10, 2018 - 13:55 , Location: Skiles 005 , Lenka Slavikova , University of Missouri , , Organizer: Michael Lacey
In this talk I will discuss the Mikhlin-H\"ormander multiplier theorem for $L^p$ boundedness of Fourier multipliers in which the multiplier belongs to a fractional Sobolev space with smoothness $s$. I will show that this theorem does not hold in the limiting case $|1/p - 1/2|=s/n$. I will also present a sharp variant of this theorem involving a space of Lorentz-Sobolev type. Some of the results presented in this talk were obtained in collaboration with Loukas Grafakos.
Wednesday, October 10, 2018 - 12:55 , Location: Skiles 006 , Josiah Park , Georgia institute of Technology , , Organizer: Galyna Livshyts
It has been known that when an equiangular tight frame (ETF) of size |Φ|=N exists, Φ ⊂ Fd (real or complex), for p > 2 the p-frame potential ∑i ≠ j | < φj, φk > |p achieves its minimum value on an ETF over all N sized collections of vectors. We are interested in minimizing a related quantity: 1/ N2 ∑i, j=1 | < φj, φk > |p . In particular we ask when there exists a configuration of vectors for which this quantity is minimized over all sized subsets of the real or complex sphere of a fixed dimension. Also of interest is the structure of minimizers over all unit vector subsets of Fd of size N. We shall present some results for p in (2, 4) along with numerical results and conjectures. Portions of this talk are based on recent work of D. Bilyk, A. Glazyrin, R. Matzke, and O. Vlasiuk.
Wednesday, October 10, 2018 - 12:20 , Location: Skiles 005 , Guillermo Goldsztein , Georgia Tech , Organizer: Trevor Gunn
In 1665, Huygens discovered that, when two pendulum clocks hanged from a same wooden beam supported by two chairs, they synchronize in anti-phase mode. Metronomes provides a second example of oscillators that synchronize. As it can be seen in many YouTube videos, metronomes synchronize in-phase when oscillating on top of the same movable surface. In this talk, we will review these phenomena, introduce a mathematical model, and analyze the the different physical effects. We show that, in a certain parameter regime, the increase of the amplitude of the oscillations leads to a bifurcation from the anti-phase synchronization being stable to the in-phase synchronization being stable. This may explain the experimental observations.
Monday, October 8, 2018 - 14:00 , Location: Skile 006 , None , None , Organizer: John Etnyre
Monday, October 8, 2018 - 14:00 , Location: Skiles 006 , Harry Richman , Univ. of Michigan , Organizer: Matt Baker
The set of (higher) Weierstrass points on a curve of genus g > 1 is an analogue of the set of N-torsion points on an elliptic curve. As N grows, the torsion points "distribute evenly" over a complex elliptic curve. This makes it natural to ask how Weierstrass points distribute, as the degree of the corresponding divisor grows. We will explore how Weierstrass points behave on tropical curves (i.e. finite metric graphs), and explain how their distribution can be described in terms of electrical networks. Knowledge of tropical curves will not be assumed, but knowledge of how to compute resistances (e.g. in series and parallel) will be useful.
Friday, October 5, 2018 - 15:05 , Location: Skiles 156 , Adrian P. Bustamante , Georgia Tech , Organizer: Adrian Perez Bustamante
In this talk I will present a proof of a generalization of a theorem by Siegel, about the existence of an analytic conjugation between an analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used to deal with small divisors problems. I will be following the work of E. Zehnder. This is a continuation of last week talk.
Friday, October 5, 2018 - 14:00 , Location: Skiles 005 , , University of Iowa , Organizer: Philipp Jell
In this talk, we introduce rather exotic algebraic structures called hyperrings and hyperfields. We first review the basic definitions and examples of hyperrings, and illustrate how hyperfields can be employed in algebraic geometry to show that certain topological spaces (underlying topological spaces of schemes, Berkovich analytification of schemes, and real schemes) are homeomorphic to sets of rational points of schemes over hyperfields.
Friday, October 5, 2018 - 13:05 , Location: Skiles 005 , , ISyE, Georgia Tech , , Organizer: He Guo
Abstract: Queueing systems are studied in various asymptotic regimes because they are hard to study in general. One popular regime of study is the heavy-traffic regime, when the system is loaded very close to its capacity. Heavy-traffic behavior of queueing systems is traditionally studied using fluid and diffusion limits. In this talk, I will present a recently developed method called the 'Drift Method', which is much simpler, and is based on studying the drift of certain test functions. In addition to exactly characterizing the heavy-traffic behavior, the drift method can be used to obtain lower and upper bounds for all loads. In this talk, I will present the drift method, and its successful application in the context of data center networks to resolve a decade-old conjecture. I will also talk about ongoing work and some open problems.   Bio: Siva Theja Maguluri is an Assistant Professor in the School of Industrial and Systems Engineering at Georgia Tech. Before that, he was a Research Staff Member in the Mathematical Sciences Department at IBM T. J. Watson Research Center. He obtained his Ph.D. from the University of Illinois at Urbana-Champaign in Electrical and Computer Engineering where he worked on resource allocation algorithms for cloud computing and wireless networks. Earlier, he received an MS in ECE and an MS in Applied Math from UIUC and a B.Tech in Electrical Engineering from IIT Madras. His research interests include Stochastic Processes, Optimization, Cloud Computing, Data Centers, Resource Allocation and Scheduling Algorithms, Networks, and Game Theory. The current talk is based on a paper that received the best publication in applied probability award, presented by INFORMS Applied probability society.
Thursday, October 4, 2018 - 13:30 , Location: Skiles 006 , Daniel Minahan , Georgia Tech , Organizer: Trevor Gunn
We discuss the construction of spectral sequences and some of their applications to algebraic geometry, including the classic Leray spectral sequence.  We will draw a lot of diagrams and try to avoid doing anything involving lots of indices for a portion of the talk.
Wednesday, October 3, 2018 - 16:30 , Location: Skiles 006 , James Anderson , Georgia Tech , Organizer: Xingxing Yu
Erdős and Nešetřil conjectured in 1985 that every graph with maximum degree Δ can be strong edge colored using at most (5/4)Δ^2 colors. In this talk we discuss recent progress made in the case of Δ=4, and go through the method used to improve the upper bound to 21 colors, one away from the conjectured 20.