Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, September 19, 2017.

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Tuesday, September 19, 2017

1:00 pm in 345 Altgeld Hall,Tuesday, September 19, 2017

No seminar

2:00 pm in 347 Altgeld Hall,Tuesday, September 19, 2017

Derivative formula for Mean-field SDEs with jumps

Yulin Song (Nanjing University and University of Illinois)

Abstract: By using Malliavin calculus for jump processes, we study the Bismut type derivative formula for Mean-field stochastic differential equations driven by L\'evy processes. Both of the derivatives with respect to a fixed initial value $x\in R^d$ and the ones with respect to an initial distribution are considered.

3:00 pm in 241 Altgeld Hall,Tuesday, September 19, 2017

Ramsey numbers of 2-interval chromatic ordered graphs

Dana Neidinger (Illinois Math)

Abstract: An ordered $G$ is a graph together with a specified linear ordering on the vertices, and its interval chromatic number is the minimum number of independent sets consisting of consecutive vertices that are needed to partition the vertex set. The $t$-color Ramsey number $R_t(G)$ of an ordered graph $G$ is the minimum number of vertices of an ordered complete graph such that every edge-coloring by $t$ colors contains a copy of $G$ in some color $i$, where the copy of $G$ preserves the original ordering on $G$. We obtain lower bounds linear in the number of vertices for the ordered Ramsey numbers of certain classes of 2-ichromatic ordered graphs using the methodology of Balko, Cibulka, Král, and Kynčl. We also determine the exact value of the $t$-color Ramsey number for two families of 2-ichromatic ordered graphs. We prove a linear upper bound for a class of 2-ichromatic ordered graphs.

3:00 pm in 243 Altgeld Hall,Tuesday, September 19, 2017

Character values, combinatorics, and some p-adic representations of finite groups

Michael Geline (Northern Illinois University)

Abstract: There are many questions which remain open from Brauer's modular representation theory of finite groups, and little agreement exists over the extent to which they ought to ultimately depend on the classification of finite simple groups. In studying a classification-free approach to one such question, involving lattices over the p-adics, I was led to an elementary combinatorial problem which is interesting in its own right and somewhat amenable to analysis by means of character values. I will present this problem, the original conjecture of Brauer which gave rise to it, and my own progress in the area. If it is necessary to mention algebraic geometry, there is something of a long-shot analogy between the character values and the Weil conjectures.