Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 13, 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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Thursday, October 13, 2016

11:00 am in 241 Altgeld Hall,Thursday, October 13, 2016

#### Analyzing rationals by simpler rationals

###### Joseph Vandehey (Ohio State)

Abstract: The (decimal) expansions of rational numbers continue to be a rather mysterious object. For instance, we expect most rational numbers to have a periodic expansion that involves a 7, but how soon should we expect that 7 to appear? In this talk, we will discuss a new method of relating the expansion of a given rational number to rationals with smaller denominators, by means of a new differencing method for exponential sums that is highly effective for exponential sums with an exponential argument.

2:00 pm in 243 Altgeld Hall,Thursday, October 13, 2016

#### Differentiability of Lipschitz maps in Euclidean spaces and Carnot groups

###### Gareth Speight (University of Cincinnati)

Abstract: Rademacher's theorem states that Lipschitz maps between Euclidean spaces are differentiable almost everywhere. Pansu's theorem asserts that the same holds for Lipschitz maps between Carnot groups. We discuss converses of these statements, where points of differentiability should be constructed inside measure zero sets. We then discuss applications of porous sets, which have relatively large holes on arbitrarily small scales, to differentiability of Lipschitz maps.

3:00 pm in 441 Altgeld Hall,Thursday, October 13, 2016

#### Construction of virtual fundamental class

###### Yun Shi (UIUC Math)

Abstract: Virtual fundamental class is an important construction for modern enumerative geometry. In this talk, I will explain the construction given by Behrend and Fantechi. I will also talk a little about its application to Donaldson-Thomas theory.

4:00 pm in 245 Altgeld Hall,Thursday, October 13, 2016

#### From Christoffel words to Markoff numbers

###### Christophe Reutenauer (Université du Québec à Montréal)

Abstract: I will present the classical theory of Markoff (1879), including its two aspects (minima of binary indefinite quadratic forms, approximation of real numbers), from the point of view of combinatorics on words.