Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, October 15, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2019          October 2019          November 2019
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  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
29 30                  27 28 29 30 31         24 25 26 27 28 29 30



Tuesday, October 15, 2019

1:00 pm in 347 Altgeld Hall,Tuesday, October 15, 2019

#### Angled crested type water waves

###### Siddhant Agrawal (U Mass Amherst)

Abstract: We consider the two-dimensional water wave equation which is a model of ocean waves. The water wave equation is a free boundary problem for the Euler equation where we assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. In the case of zero surface tension, we show that the singular solutions recently constructed by Wu (19) are rigid. In the case of non-zero surface tension, we construct an energy functional and prove a local wellposedness result without assuming the Taylor sign condition. This energy reduces to the energy obtained by Kinsey and Wu (18) in the zero surface tension case and allows angled crest interfaces. For non zero surface tension, the energy does not allow singularities in the interface but allows interfaces with large curvature. We show that in an appropriate regime, the zero surface tension limit of our solutions is a solution of the gravity water wave equation which includes waves with angled crests.

2:00 pm in 243 Altgeld Hall,Tuesday, October 15, 2019

#### Equiangular lines with a fixed angle

###### Zilin Jiang (MIT Math)

Abstract: An equiangular set of lines is a family of lines (through the origin) such that they are pairwise separated by the same angle. A central question in Algebraic Graph Theory is to determine the maximum cardinality of an equiangular set of lines in n-dimensional Euclidean space. In this talk, we will prove the key spectral result on the multiplicity of the second largest eigenvalue of a connected graph, and we will then connect it to the question on equiangular lines. Joint work with Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao.

2:00 pm in 347 Altgeld Hall,Tuesday, October 15, 2019

#### On the spectral heat content for subordinate killed Brownian motions with respect to a wide class of subordinators

###### Hyunchul Park (SUNY New Paltz)

Abstract: In this talk, we study the asymptotic behavior of the spectral heat content for subordinate killed Brownian motions (SKBM) with respect to a wide class of subordinators. Previously, the spectral heat content for SKBM via stable subordinators was studied by the author and R. Song. This result gives an upper bound for the heat loss for the spectral heat content for killed Levy processes, whose asymptotic limit is not available for $\mathbb{R}^d$, $d\ge 2$, even for killed $\alpha$-stable processes when $\alpha\in [1; 2)$. This is a joint work with R. Song and is in progress.

3:00 pm in 243 Altgeld Hall,Tuesday, October 15, 2019

#### Koszul Modules and Green’s Conjecture

###### Claudiu Raicu (University of Notre Dame)

Abstract: Formulated in 1984, Green’s Conjecture predicts that one can recognize the intrinsic complexity of an algebraic curve from the syzygies of its canonical embedding. Green’s Conjecture for a general curve has been resolved in two landmark papers by Voisin in the early 00s. I will explain how the recent theory of Koszul modules provides more elementary solutions to this problem, by relating it to the study of the syzygies of some very concrete surfaces. Joint work with M. Aprodu, G. Farkas, S. Papadima, S. Sam and J. Weyman.