Department of

Mathematics


Seminar Calendar
for events the day of Friday, September 21, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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                        30                                         

Friday, September 21, 2018

3:00 pm in 345 Altgeld Hall,Friday, September 21, 2018

Implications of Time-Varying War Risk

Gertjan Verdickt (University of Antwerp)

3:00 pm in 145 Altgeld Hall,Friday, September 21, 2018

Decay of cone averages of the Fourier transform

Terence Harris (Illinois Math)

Abstract: I will give an introduction to the techniques of decoupling and induction on scales from harmonic analysis, and then describe how they relate to the average $L^2$ decay over the cone of the Fourier transform of fractal measures.

4:00 pm in 241 Altgeld Hall,Friday, September 21, 2018

The geometry of some low dimensional Lie groups

Ningchuan Zhang (UIUC)

Abstract: In this talk, I'll give explicit geometric descriptions of some low dimensional matrix groups. The goal is to show $\mathrm{SU}(2)\simeq S^3$ is a double cover of $\mathrm{SO}(3)$ and $\mathrm{SL}_2(\mathbb{C})$ is a double cover of the Lorentz group $\mathrm{SO}^+(1,3)$. Only basic knowledge of linear algebra and topology is assumed.

4:00 pm in 245 Altgeld Hall,Friday, September 21, 2018

Computer Driven Questions and Theorems in Geometry

Moira Chas (Stony Brook)

Abstract: Three numbers can be associated to a deformation class of closed curves on a surface S:

- the self-intersection number (this is the smallest number of times a representative of the curve crosses itself),
- the word length (that is the smallest number of letters, in a certain alphabet chosen apriori, one needs to describe the class ) and
- the length of the geodesic in the class (this is the length of the shortest representative of the class, where the way of computing length is chosen beforhand).

The interrelations of these three numbers exhibit many patterns when explicitly determined or approximated using algorithms and a computer. We will discuss how these computations can lead to counterexamples of existing conjectures, to the discovery of new conjectures and to subsequent theorems in some cases.