Seminar Calendar
for events the week of Sunday, August 28, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, August 29, 2016

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, August 29, 2016
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Submitted by laugesen.
Chris Leininger (Department of Mathematics, University of Illinois)
Mapping class groups
Abstract: After recalling the classification of surfaces, I will explain what the mapping class group of a surface is, why it's important, and some of the tools and techniques used to study it.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, August 29, 2016
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Submitted by mjunge.
Marius Junge (UIUC)
Organizational meeting
Abstract: We collect interesting topics and speakers.

Tuesday, August 30, 2016

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, August 30, 2016
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Submitted by vesna.
Mark Behrens (University of Notre Dame)
Perspectives on the telescope conjecture
Abstract: Mahowald-Ravenel-Schick attempted to disprove the telescope conjecture using the localized Adams spectral sequence, and described a very precise hypothesis. I will describe work, with Beaudry-Bhattacharya-Culver-Ravenel-Xu, where we consider what the unlocalized tmf-resolution, and the motivic localized Adams spectral sequence have to say about the telescope. While these tools alone don't seem to resolve the conjecture, they do make the MRS hypothesis eminently believable.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, August 30, 2016
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Submitted by ssolecki.
Jan Foniok (Manchester Metropolitan University)
On adjoint functors in the categories of graphs and digraphs
Abstract: We consider the category of digraphs and their homomorphisms, as well as its full subcategory of graphs and several variations. These adjunctions have many applications in areas such as graph colouring and computational complexity of constraint satisfaction problems. I will present a characterisation and discuss some of the applications and some open problems. Examples include: a simple proof that deciding the existence of a homomorphism to C_5 is NP-complete; a circular Gallai-Roy theorem; Hedetniemi's conjecture (that the chromatic number of the product of two graphs is equal to the minimum of the chromatic numbers of the factors). Much of the content is based on joint work with Claude Tardif.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, August 30, 2016
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Submitted by molla.
Jozsef Balogh (Illinois Math)
Some applications of the container method in discrete geometry
Abstract: The container method proved to be applicable in several areas of combinatorics. I will discuss some new applications. 1. We consider a problem of Erdos about point sets in the plane in (almost) general position. 2. We discuss epsilon-nets, where the underlying set is a subset of points in the plane, and the ranges are collinear point tuples. Though we have not completely solved any of the problems, maybe our improvements are of some interests. It is joint work with Jozsef Solymosi.

Wednesday, August 31, 2016

Graduate Panel Discussion
4:00 pm   in 350 Altgeld (Conference Room),  Wednesday, August 31, 2016
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Submitted by kmortens.
Life After Comps
Abstract: A panel discussion about the transition from primarily coursework to primarily research. For all PhD students who have recently completed comps or who are nearing the completion of comps.


5:00 pm   in 245 Altgeld Hall,  Wednesday, August 31, 2016
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Submitted by tyson.
IGL Outreach Information Session
Abstract: Information session about outreach opportunities and training with the Illinois Geometry Lab.

Thursday, September 1, 2016

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, September 1, 2016
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Submitted by sahlgren.
Junxian Li (Illinois Math)
A lower bound for the least prime in an arithmetic progression
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 $\liminf_{k} \frac{P(k)}{ \phi(k) \log^2 k} = 1$.

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in Altgeld Hall 243,  Thursday, September 1, 2016
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Submitted by kapovich.
Tomasz Mrowka (Massachusetts Institute of Technology)
Gauge theory for webs and foams
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.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, September 1, 2016
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Submitted by kapovich.
Tomasz Mrowka (Massachusetts Institute of Technology)
An approach to the Four Color Theorem via Gauge Theory
Abstract: This is the 40th anniversary of the Appel and Haken proof that four colors suffice to color any planar maps. Their 1976 proof was particularly notable for its reliance on computers in a serious manner. A few years ago Peter Kronheimer and I realized that some of the invariants of knots in three manifolds coming from gauge theory had a generalization to invariants of knotted trivalent graphs. One of these invariants plausibly can be used to attack the four color theorem. In this talk I will sketch in rather broad terms some of these ideas. These invariants connect the four color problem to an important line of work combining gauge theory and 3 dimensional topology (where Haken's work provided an important foundation.)

Friday, September 2, 2016

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, September 2, 2016
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Submitted by anush.
Anton Bernshteyn (UIUC Math)
On "Regularity lemma for distal structures" by A. Chernikov and S. Starchenko

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, September 2, 2016
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Submitted by dcarmod2.
Daniel Carmody (UIUC Math)
An Introduction to Algebraic K_1 and K_2
Abstract: I'll give a brief introduction to K-theory by recalling the definition of K_0 of a ring and some of its basic properties. Then, I'll define K_1 and K_2 and explain the somewhat surprising fact that these groups fit into a cohomology theory.