# Discrete Math Seminar (DMS)

The **Discrete Math Seminar (DMS)** is a research seminar intended for Kennesaw State faculty working in the various
fields of algebra, number theory, and discrete math. A main goal of the seminar is
to encourage collaborative work between KSU and neighboring institutions. Seminars
often involved advanced mathematical knowledge. However, the seminars are open to
anyone who is interested in attending.

**Unless specified otherwise, seminars are held every other Monday from 2:00-3:00pm in D-249 on the Marietta Campus.*

**Spring 2018**

**Monday, February 19, 2018**

**Ahmad Peivandi**, Georgia State University

*"Assignment Problems with Complementarities"*- ABSTRACT: The problem of allocating bundles of indivisible objects without transfers
arises in the assignment of courses to students, of computing resources like CPU time,
memory and disk space to computing tasks and the truck loads of food to food banks.
In these settings the complementarities in preferences are small compared with the
size of the market. We exploit this to design mechanisms satisfying efficiency, envy-freeness
and asymptotic strategy-proofness.

Informally, we assume that agents do not want bundles that are too large. There will be a parameter*k*such that the marginal utility of any item relative to a bundle of size*k*or larger is zero. We call such preferences*k*-demand preferences. Given this parameter we show how to represent probability shares over bundles as lotteries over approximately (deterministic) feasible integer allocations. The degree of infeasibility in these integer allocations will be controlled by the parameter*k*. In particular, ex-post, no good is over allocated by at most*k-1*units.

**Monday, March 5, 2018**

**David Clark**, Grand Valley State University

**Monday, March 19, 2018**

- Infinite Horizons Lecture

**Monday, April 9, 2018**

- TBA

**Monday, April 23, 2018**

- TBA

**Fall 2017**

***Friday, September 22, 2017* - SPECIAL TIME/LOCATION - 1:00-2:00pm in MS 006 on the Kennesaw campus**

**Axel Brandt**, Davidson College*"Optimization, Probability, and Modeling as a tool in Extremal Graph Theory"*- ABSTRACT: Similar to optimization, questions in extremal graph theory ask for a maximum or minimum of a parameter under certain constraints. Although convex programming provides a powerful tool to solve numerical optimization questions, questions in extremal graph theory have historically been approached by ingenuity and trial-and-error. Recently, Razborov developed the theory of flag algebras, which provides a method of translating an extremal graph theory problem to a semidefinite programming problem. In this talk, we will explore the process of this translation.

**Friday, October 20, 2017 - SPECIAL TIME- 1:30-2:30pm**

**Babak Moazzez**, Kennesaw State University*"Spread of Influence in Graphs via Integer Programming: A polyhedral Study"*- ABSTRACT: Spread of influence in a network can be modeled and studied within the concept of dynamic monopolies in graphs. We give an integer programming formulation for finding a minimum dynamic monopoly in an undirected graph. The corresponding 0-1 polytope and its facets are studied and several families of facet defining inequalities are introduced. Computational experiments have been performed to show the strength of the IP formulation and its facet defining inequalities.