Department of

Mathematics

Seminar Calendar
for events the day of Thursday, September 1, 2016.

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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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1  2  3  4  5  6                1  2  3                      1
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30 31


Thursday, September 1, 2016

11:00 am in 241 Altgeld Hall,Thursday, September 1, 2016

A lower bound for the least prime in an arithmetic progression

Junxian Li (Illinois Math)

Abstract: Fix $k$ a positive integer, and let $\ell$ be coprime to $k$. Let $p(k,\ell)$ denote the smallest prime equivalent to $\ell \pmod{k}$, and set $P(k)$ to be the maximum of all the $p(k,\ell)$. We seek lower bounds for $P(k)$. In particular, we show that for almost every $k$ one has $P(k) \gg \phi(k) \log k \log_2 k \log_4 k / \log_3 k,$ answering a question of Ford, Green, Konyangin, Maynard, and Tao. We rely on their recent work on large gaps between primes. Our main new idea is to use sieve weights to capture not only primes, but also small multiples of primes. We also give a heuristic which suggests that $\liminf_{k} \frac{P(k)}{ \phi(k) \log^2 k} = 1$. This is joint work with Kyle Pratt and George Shakan.

12:00 pm in Altgeld Hall 243,Thursday, September 1, 2016

Gauge theory for webs and foams

Tomasz Mrowka (Massachusetts Institute of Technology)

Abstract: I will discuss how to use Instanton Floer theory ideas to construct invariants of Webs (knotted trivalent graphs) in the three manifolds. These invariants are functorial for Foam cobordisms. The talk will the discuss some properties of these invariants and some computational tools. A particular variant of this story might be applicable lead to a non-computer aided proof of the four color theorem.

3:00 pm in 243 Altgeld Hall,Thursday, September 1, 2016

Organizational Meeting

3:00 pm in 441 Altgeld Hall,Thursday, September 1, 2016

Abstract: Among other things, the ADE Dynkin diagrams classify: finite subgroups of $SL_2(\mathbb{C})$ (McKay correspondence); isolated surface singularities with multiplicity 2 that can be resolved by successive blowups (Kleinian/du Val singularities); and some complex simple Lie algebras (Killing-Cartan/Dynkin classfication). I'll tell you a story about how these three families are tied together in the geometry of the Grothendieck-Springer resolution and Slodowy slices.