## Seminars and Colloquia Schedule

### A Self-Limiting Hawkes Process

Series
SIAM Student Seminar
Time
Monday, November 16, 2020 - 12:30 for 1 hour (actually 50 minutes)
Location
ONLINE at https://bluejeans.com/703668715
Speaker
John OlindeGT Math

Many real life processes that we would like to model have a self-exciting property, i.e. the occurrence of one event causes a temporary spike in the probability of other events occurring nearby in space and time.  Examples of processes that have this property are earthquakes, crime in a neighborhood, or emails within a company.  In 1971, Alan Hawkes first used what is now known as the Hawkes process to model such processes.  Since then much work has been done on estimating the parameters of a Hawkes process given a data set and creating variants of the process for different applications.

In this talk, I will be proposing a new variant of a Hawkes process that takes into account the effect of police activity on the underlying crime rate and an algorithm for estimating its parameters given a crime data set.

### TBA by Ian Runnels

Series
Geometry Topology Seminar
Time
Monday, November 16, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Ian RunnelsUniversity of Virginia

### PDE Models for Collective Behavior

Series
Time
Monday, November 16, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Bluejeans meeting: https://gatech.bluejeans.com/759112674
Speaker
Dr. Yao YaoGeorgia Institute of Technology

Self-organization is a common feature in the collective behavior of many animal species, such as flocking birds, herding mammals, and swarming bacteria. As the number of individuals gets large, instead of tracking the movement of each individual, it is more efficient to model the evolution of the whole population density using partial differential equations (PDEs). In this talk, I will introduce some PDE models for collective dynamics, and discuss the challenges in both the modeling part and the mathematical analysis.

### Pointwise ergodic theorems for bilinear polynomial averages

Series
Analysis Seminar
Time
Tuesday, November 17, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09
Speaker
Mariusz MirekRutgers University

We shall discuss the proof of pointwise almost everywhere convergence for the non-conventional (in the sense of Furstenberg) bilinear polynomial ergodic averages. This is my recent work with Ben Krause and Terry Tao.

### Transversal $C_k$-factors in subgraphs of the balanced blowup of $C_k$

Series
Graph Theory Seminar
Time
Tuesday, November 17, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Theo MollaUniversity of South Florida

Call a blowup of a graph $F$ an $n$-blowup if each part has size $n$. For a subgraph $G$ of a blowup of $F$, we define the minimum partial degree of $G$ to be the smallest minimum degree over the bipartite subgraphs of $G$ that correspond to edges of $F$. Johannson proved that if the minimum partial degree of a spanning subgraph of the $n$-blowup of a triangle is $2n/3 + n^{1/2}$, then it contains a collection of $n$ vertex disjoint triangles. Fischer's Conjecture, which was proved by Keevash and Mycroft in 2015, is a generalization of this result to complete graphs larger than the triangle. Another generalization, conjectured independently by Fischer and Häggkvist, is the following: If $G$ is a spanning subgraph of the $n$-blowup of $C_k$ with minimum partial degree $(1 + 1/k)n/2 + 1$, then $G$ contains $n$ vertex disjoint copies of $C_k$ that each intersect each of the $k$ parts. In this talk, we will show that this conjecture holds asymptotically. We will also discuss related conjectures and results.

This is joint work with Beka Ergemlidze.

### Grid Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, November 18, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
online
Speaker
Sally Collins

Grid homology is a purely combinatorial description of knot Floer homology in which the counting of psuedo-holomorphic disks is replaced with a counting of polygons in grid diagrams. This talk will provide an introduction to this theory, and is aimed at an audience with little to no experience with Heegaard Floer homology.

### Hodge theory for tropical varieties 2

Series
Algebra Seminar
Time
Wednesday, November 18, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Omid Amini

Part 2 of 3-part series

The aim of these two talks is to give an overview of our work on tropical Hodge theory. We show that cohomology groups of smooth projective tropical varieties verify hard Lefschetz property and Hodge-Riemann relations. Providing a description of the Chow groups of matroids in terms of cohomology groups of specific smooth projective tropical varieties, these results can be regarded as a generalization of the work of Adiprasito-Huh-Katz to more general tropical varieties. We also prove that smooth projective tropical varieties verify the analogue in the tropical setting of the weight-monodromy conjecture, affirming a conjecture of Mikhalkin and Zharkov.

### New Classes of Multivariate Covariance Functions

Series
Stochastics Seminar
Time
Thursday, November 19, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://gatech.webex.com/gatech/j.php?MTID=mee147c52d7a4c0a5172f60998fee267a
Speaker
Tatiyana ApanasovichGeorge Washington University

The class which is refereed to as the Cauchy family allows for the simultaneous modeling of the long memory dependence and correlation at short and intermediate lags. We introduce a valid parametric family of cross-covariance functions for multivariate spatial random fields where each component has a covariance function from a Cauchy family. We present the conditions on the parameter space that result in valid models with varying degrees of complexity. Practical implementations, including reparameterizations to reflect the conditions on the parameter space will be discussed. We show results of various Monte Carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging. The application of the proposed multivariate Cauchy model is illustrated on a dataset from the field of Satellite Oceanography.

Link to Cisco Webex meeting: https://gatech.webex.com/gatech/j.php?MTID=mee147c52d7a4c0a5172f60998fee267a

### TBA by Siddhi Krishna

Series
Research Horizons Seminar
Time
Friday, November 20, 2020 - 12:30 for 1 hour (actually 50 minutes)
Location
Microsoft Teams
Speaker
Siddhi KrishnaGeorgia Tech

### Prague dimension of random graphs

Series
ACO Student Seminar
Time
Friday, November 20, 2020 - 13:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Kalen PattonMath, Georgia Tech

Various notions of dimension are important throughout mathematics, and for graphs the so-called Prague dimension was introduced by Nesetril, Pultr and Rodl in the 1970s. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order $n/\log n$ for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size $O(\log n)$.

Based on joint work with He Guo and Lutz Warnke.