Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 30, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2015             April 2015              May 2015
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7             1  2  3  4                   1  2
8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
15 16 17 18 19 20 21   12 13 14 15 16 17 18   10 11 12 13 14 15 16
22 23 24 25 26 27 28   19 20 21 22 23 24 25   17 18 19 20 21 22 23
29 30 31               26 27 28 29 30         24 25 26 27 28 29 30
31


Thursday, April 30, 2015

11:00 am in 241 Altgeld Hall,Thursday, April 30, 2015

#### Sums of Euler products and statistics of elliptic curves

###### Dimitrios Koukoulopoulos (Univ. Montreal)

Abstract: I will present a new approach to several statistical questions about elliptic curves over finite fields, such as the average Lang-Trotter conjecture and the vertical Sato-Tate conjecture. The starting point is a theorem of Gekeler that provides a probabilistic reinterpretation of Deuring's theorem about the number of elliptic curves in a given isogeny class. In the heart of our approach lies a general technical theorem about averages of Euler products. As a corollary of this general result, we obtain new proofs of various results, some already known and some of which are new. One of the new results is the vertical Sato-Tate conjecture for very short intervals. This is joint work with Chantal David and Ethan Smith.

1:00 pm in Altgeld Hall 243,Thursday, April 30, 2015

#### A new continuity flow of Monge-Ampere type, Gromov-Hausdorff limits and Minimal Model program

###### Gabriel La Nave (UIUC Math)

Abstract: I will describe a new continuity equation recently introduced by G.Tian and myself and it's connection with then Minimal Model Program. In particular, in joint work with Tian and Z. Zhang, we show that the Gromov-Hausdorff of our continuity method are homeomorphic to a normal projective variety and that the singularities of the metric are concentrated on a sub variety , under some natural assumptions --which are the natural differential geometric versions of the assumptions in Kawamata's base point free theorem

3:00 pm in 243 Altgeld Hall,Thursday, April 30, 2015

#### Hyperplane arrangements, resonance varieties, and the zero-divisor cup length

###### Nathan Fieldsteel (UIUC Math)

Abstract: For an $R$-algebra $A$, the zero-divisor cup length of $A$ is the maximum length of a non-zero product in the ideal of zero divisors in $A \otimes_R A$. We are interested in the zero-divisor cup length in the case where $A$ is the Orlik-Solomon algebra of a hyperplane arrangement. For generic arrangements we would like to confirm a conjecture, due to Yuzvinsky, that gives a formula for the zero-divisor cup length. For non-generic arrangements, we would like a geometric or combinatorial predictor of when the zero-divisor cup length is "lower than expected", hopefully in terms of the resonance varieties of the arrangement. We will demonstrate the utility of Macaulay2 in performing computations related to these questions.

4:00 pm in 245 Altgeld Hall,Thursday, April 30, 2015

#### Spring Department Faculty Meeting

Abstract: The Spring Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 239 Altgeld Hall.