Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 29, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, March 29, 2018

11:00 am in 241 Altgeld Hall,Thursday, March 29, 2018

#### Around Vinogradov's three primes theorem

###### Fernando Shao (U Kentucky Math)

Abstract: Vinogradov showed in 1937 that every large enough odd integer can be represented as a sum of three primes. One may ask what if these primes are restricted to some (potentially sparse) subset of the primes. In general, if the set is badly distributed in congruence classes or Bohr sets, the result does not necessarily hold. In this talk I will describe two "transference type'' results aimed to show the obstructions described above are the only obstructions. As applications, we get that Vinogradov's three primes theorem holds for Chen primes and for primes in short intervals. This is based on joint works with K. Matomaki and J. Maynard.

1:00 pm in 347 Altgeld Hall,Thursday, March 29, 2018

#### Variable immunity and its consequences for disease

###### Tara Stewart (Animal Biology, UIUC)

Abstract: Infectious disease results from interactions between pathogens and susceptible hosts in the environment. For many populations, we have a limited understanding of the mechanisms that shape host susceptibility and how these mechanisms interact with ecological factors to regulate the spread of disease. Focusing on a simple one-host one-parasite system with environmental transmission, I use theoretical and empirical methods to explore the causes and consequences of variable host immunity. I demonstrate how integrating immune defenses into host-parasite interactions can improve our understanding of disease transmission in natural systems.

2:00 pm in 241 Altgeld Hall,Thursday, March 29, 2018

#### Restriction estimates and their applications in number theory

###### Fernando Xuancheng Shao   [email] (University of Kentucky)

Abstract: I will survey recent developments on restriction theory for exponential sums over sets of number theoretic interest, such as primes, smooth numbers, and k-th powers, and their applications to analytic number theory and additive combinatorics, including Roth-type theorems in primes and Waring-type results in smooth k-th powers.

3:00 pm in 243 Altgeld Hall,Thursday, March 29, 2018

#### An algorithm for volumes of polytopes with applications to social choice

###### Winfried Bruns (Universität Osnabrück)

Abstract: We discuss a fast algorithm for the computation of the volume of rational polytopes with few (nonsimplicial) facets. It is based on a natural recursive approach, originally suggested by Lasserre, that uses descent in the face lattice. For efficient computations in high dimensions it needs a sophisticated implementation that has now been realized in Normaliz. Probabilities in social choice that are based on the Impartial Anonymous Culture can often be interpreted as volumes of rational polytopes. For 4 candidates these polytopes have dimension 24, and the computation is a challenge. Before the new algorithm had been implemented, Normaliz had to use triangulations. Descent in the face lattice makes all these computations very easy and gives access to many more that hitherto had been inaccessible.

4:00 pm in 245 Altgeld Hall,Thursday, March 29, 2018