Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 8, 2018.

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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, March 8, 2018

11:00 am in Siebel 1103,Thursday, March 8, 2018

#### Some generalizations of prime number races problems

###### Xianchang Meng (McGill Math)

Abstract: Chebyshev observed that there seems to be more primes congruent to 3 mod 4 than those congruent to 1 mod 4, which is known as Chebyshev’s bias. In this talk, we introduce two generalizations of this phenomenon. 1) Greg Martin conjectured that the difference of the summatory function of the number of prime factors over integers less than x from different arithmetic progressions will attain a constant sign for sufficiently large x. Under some reasonable conjectures, we give strong evidence to support this conjecture. 2) We introduce the function field version of Chebyshev’s bias. We consider the distribution of products of irreducible polynomials over finite fields. When we compare the number of such polynomials among different arithmetic progressions, new phenomenon will appear due to the existence of real zeros for some associated L-functions.

2:00 pm in Altgeld Hall,Thursday, March 8, 2018

#### Cancelled

2:00 pm in 243 Altgeld Hall,Thursday, March 8, 2018

#### Variations on the Mean Value Property

###### Jose Gonzalez-Llorente (Universidad Autonoma de Barcelona)

Abstract: The fruitful interplay between Geometric Function Theory, Potential Theory and Probability relies on the well known Mean Value Property for harmonic functions. In the last years substantial efforts have been made to clarify the probabilistic framework associated to some relevant nonlinear differential operators (such as the $p$-laplacian or the infinity laplacian) by means of appropriate (nonlinear) mean value properties. In the talk we will review some classical facts about the converse mean value property and also some more recent results about nonlinear mean value properties related to the $p$-laplacian.

3:00 pm in 322 David Kinley Hall,Thursday, March 8, 2018

#### Ideals of QSym, shuffle-compatibility and exterior peaks

###### Darij Grinberg (U. Minnesota)

Abstract: In recent work (arXiv:1706.00750), Gessel and Zhuang have introduced the concept of a shuffle-compatible permutation statistic, and shown that various "descent statistics" (e.g., the descent set, the descent number, the major index, the peak set, the peak number) are shuffle-compatible. Every such statistic leads to an ideal of the algebra QSym of quasisymmetric functions. I shall discuss one particular statistic -- the "exterior peak set" -- whose shuffle-compatibility I prove (it was left open by Gessel and Zhuang). I will then proceed to extend the notion of shuffle-compatibility to a stronger notion that distinguishes between left and right shuffles. Proving that the exterior peak set still satisfies this stronger version of shuffle-compatibility leads us through several algebraic structures on QSym: the Hopf antipode, the dendriform structure, and two further operations. (Preprint: http://www.cip.ifi.lmu.de/~grinberg/algebra/gzshuf2.pdf )

4:00 pmThursday, March 8, 2018