Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 14, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2017            March 2017             April 2017
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             1  2  3  4                      1
5  6  7  8  9 10 11    5  6  7  8  9 10 11    2  3  4  5  6  7  8
12 13 14 15 16 17 18   12 13 14 15 16 17 18    9 10 11 12 13 14 15
19 20 21 22 23 24 25   19 20 21 22 23 24 25   16 17 18 19 20 21 22
26 27 28               26 27 28 29 30 31      23 24 25 26 27 28 29
30


Tuesday, March 14, 2017

11:00 am in 241 Altgeld Hall,Tuesday, March 14, 2017

#### In the neighbourhood of Sato-Tate conjecture

###### Sudhir Pujahari (Harish-Chandra Research Institute)

Abstract: In this talk, we will see the distribution of gaps between eigenangles of Hecke operators acting on the space of cusp forms of weight $k$ and level $N$, spaces of Hilbert modular forms of weight $k = (k_1, k_2,\ldots , k_r)$ and space of primitive Maass forms of weight $0$. Moreover, we will see the following: Let $f_1$ and $f_2$ be two normalized Hecke eigenforms of weight $k_1$ and $k_2$ such that one of them is not of CM type. If the set of primes $\mathcal{P}$ such that the $p$-th coefficients of $f_1$ and $f_2$ matches has positive upper density, then $f_1$ is a Dirichlet character twist of $f_2$. The last part is a joint work with M. Ram Murty.

12:00 pm in 243 Altgeld Hall,Tuesday, March 14, 2017

#### Flat submaps in CAT(0) $(p,q)$-maps and maps with angles

###### Mark Sapir (Vanderbilt and Illinois Math)

Abstract: This is a joint work with A. Olshanskii. Let $p, q$ be positive integers with $1/p+1/q=1/2$. We prove that if a $(p,q)$-map $M$ does not contain flat submaps of radius $\ge r$, then its area does not exceed $c(r+1)n$ where $n$ is the perimeter of $M$ and $c$ is an absolute constant. Earlier Ivanov and Schupp proved an exponential bound in terms of $r$. We prove an estimate similar to Ivanov and Schupp for much more general maps with angles" which include, for example, van Kampen diagrams over the presentation of the Baumslag-Solitar group $BS(1,2)$ and many groups corresponding to $S$-machines. We also show that a $(p,q)$ map $M$ tessellating a plane ${\mathbb R}^2$ has path metric quasi-isometric to the Euclidean metric on the plane if and only if $M$ has only finitely many non-flat vertices and faces.

1:00 pm in Altgeld Hall,Tuesday, March 14, 2017

#### Model theory and Painleve equations

###### James Freitag (UIC Math)

Abstract: We will discuss how to use model theory to prove some transcendence results for solutions of Painleve equations.

2:00 pm in 347 Altgeld Hall,Tuesday, March 14, 2017

#### On random multiplicative functions

###### Joseph Najnudel (University of Cincinnati)

Abstract: In this talk, we give a presentation of random multiplicative functions on the integers and their main properties. At the end of the talk, we state some results, proven in a preprint recently submitted, on the behaviour and the independence properties of such functions taken at consecutive integers.

3:00 pm in 243 Altgeld Hall,Tuesday, March 14, 2017

#### Categorical Gromov-Witten Invariants

###### Junwu Tu (University of Missouri )

Abstract: In this talk, following Costello and Kontsevich, we describe a construction of Gromov-Witten type invariants from cyclic A-infinity categories.

3:00 pm in 241 Altgeld Hall,Tuesday, March 14, 2017

#### Rooted forests that avoid sets of permutations

###### Katherine Anders (The University of Texas at Tyler)

Abstract: An unordered rooted labeled forest avoids the pattern $\pi\in\mathcal{S}_n$ if the sequence obtained from the labels along the path from the root to any vertex does not contain a subsequence that is in the same relative order as $\pi$. We enumerate several classes of forests that avoid certain sets of permutations, including the set of unimodal forests, via bijections with set partitions with certain properties. This is joint work with Kassie Archer.

5:00 pm in 314 Altgeld Hall,Tuesday, March 14, 2017

#### IGL Midsemester Meeting

Abstract: IGL research groups will give short presentations on their work. Come see what has been going on in the IGL this semester!