Department of

Mathematics


Seminar Calendar
for events the day of Thursday, November 29, 2018.

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Thursday, November 29, 2018

11:00 am in 241 Altgeld Hall,Thursday, November 29, 2018

Fourier optimization and primes in short intervals

Micah Milinovich (University of Mississippi Math)

Abstract: I will discuss the proofs of the strongest known asymptotic and explicit estimates in the classical problem of bounding the maximum gap between consecutive primes assuming the Riemann hypothesis. These proofs involve three main ingredients: the explicit formula relating the primes to the zeros of the Riemann zeta-function, the size of the constant in the Brun-Titchmarsh inequality, and Fourier optimization. I will also discuss how to use Fourier optimization, in particular the solution to the Beurling-Selberg extremal problem for the Poisson kernel, to estimate the variance of primes on short intervals sharpening the previous results of Selberg, Montgomery, Gallagher and Mueller, Goldston and Gonek, and others. This talk is based on joint works with E. Carneiro, V. Chandee, A. Chirre, and K. Soundararajan.

12:30 pm in 464 Loomis,Thursday, November 29, 2018

To Be Announced

Netta Engelhardt (Princeton University)

2:00 pm in 241 Altgeld,Thursday, November 29, 2018

Fourier Analysis and the zeros of the Riemann zeta-function

Micah B. Milinovich (U. of Mississippi Math)

Abstract: I will show how the classical Beurling-Selberg extremal problem in harmonic analysis arises naturally when studying the vertical distribution of the zeros of the Riemann zeta-function and other L-functions. Using this relationship, along with techniques from Fourier analysis and reproducing kernel Hilbert spaces, we can prove the sharpest known bounds for the number of zeros in an interval on the critical line and we can also study the pair correlation of zeros. Our results on pair correlation extend earlier work of P. X. Gallagher and give some evidence for the well-known conjecture of H. L. Montgomery. This talk is based on a series of papers that are joint with E. Carneiro, V. Chandee, and F. Littmann.

3:00 pm in 345 Altgeld Hall,Thursday, November 29, 2018

Orbital Varieties and Conormal Varieties

Rahul Singh   [email] (Northeastern University)

Abstract: I will start by recalling Steinberg's geometric interpretation of the Robinson-Schensted correspondence and use that as a point of introduction to orbital varieties and conormal varieties of Schubert varieties. The main focus of the talk will be the combinatorics and geometry of these varieties when the underlying Schubert variety is cominuscule. In particular, I will present some recent work constructing a resolution of singularities and a system of defining equations. Time permitting, we will also discuss some geometric results in the case where the underlying Schubert variety is a divisor. There will be a pre-talk at 12:30 PM in 441 Altgeld Hall titled "Robinson-Schensted correspondence with a geometric flavor". Abstract: We index the irreducible components of the Steinberg variety in two different ways, once by the symmetric group S_n, and once by pairs of (standard) Young tableaux. This 'naturally' recovers the Robinson-Schensted correspondence. This setup also provides the 'geometric order' on Young tableaux, which remains combinatorially mysterious in its full generality.

4:00 pm in 245 Altgeld Hall,Thursday, November 29, 2018

Primality testing: then and now

Carl Pomerance (Dartmouth College)

Abstract: The task is simply stated. Given a large integer, decide if it is prime or composite. Gauss wrote of this algorithmic problem (and the twin task of factoring composites) in 1801: "the dignity of science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated." Though progress with factoring composites has been steady and substantial, I think Gauss would be especially pleased with the enormous progress in primality testing, both in practice and in theory. In fact, one of the latest developments strangely and aptly employs a construct Gauss used to deal with ruler and compass constructions of regular polygons! This talk will present a survey of some of the principal ideas used in the prime recognition problem starting with the 19th century work of Lucas, to the 21st century work of Agrawal, Kayal, and Saxena, and beyond.