TBA

Ioana Dumitriu

UC San Diego

Time:

Monday, December 6, 2021 - 12:00pm

Zoom

Large deviations for triangle densities

Joe Neeman

UT Austin

Time:

Monday, November 29, 2021 - 12:00pm

Location:

Zoom ID 989 6529 0738. Passcode: the last four digits of the zoom ID in the reverse order

Take a uniformly random graph with a fixed edge density e. Its triangle density will typically be about e^3, and we are interested in the large deviations behavior: what's the probability that the triangle density is about e^3 - delta? The general theory for this sort of problem was studied by Chatterjee-Varadhan and Dembo-Lubetzky, who showed that the solution can be written in terms of an optimization over certain integral kernels. This optimization is difficult to solve explicitly, but Kenyon, Radin, Ren and Sadun used numerics to come up with a fascinating and intricate set of conjectures regarding both the probabilities and the structures of the conditioned random graphs. We prove these conjectures in a small region of the parameter space.

TBA

Marcin Bownik

Institution:

University of Oregon

Time:

Monday, November 22, 2021 - 12:00pm

Zoom

TBA

Speaker:

Stefanie Petermichl

Institution:

Universität Würzburg

Time:

Monday, November 8, 2021 - 12:00pm

Zoom

TBA

Brett Wick

Institution:

Washington University in St. Louis

Time:

Monday, November 1, 2021 - 12:00pm

Zoom

TBA

Speaker:

Pavel Zorin-Kranich

Institution:

University of Bonn

Time:

Monday, October 25, 2021 - 12:00pm

Zoom

TBA

Cristina Benea

Institution:

University of Nantes

Time:

Monday, October 18, 2021 - 12:00pm

Zoom

Strong asymptotic freeness for independent uniform variables on compact groups

Speaker:

Charles Bordenave

Institution:

Institute of Mathematics of Marseille

Time:

Monday, October 11, 2021 - 12:00pm

Location:

Zoom

Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of random unitaries and strong asymptotic freeness of random permutations acting on the orthogonal of the Perron-Frobenius eigenvector. In this talk, we consider a new matrix unitary model appearing naturally from representation theory of compact groups. We fix a non-trivial signature, i.e. two finite sequences of non-increasing natural numbers, and for n large enough, consider the irreducible representation of Un associated to this signature. We show that strong asymptotic freeness holds in this generalized context when drawing independent copies of the Haar measure. We also obtain the orthogonal variant of this result. This is a joint work with Benoît Collins.

To see zoom ID and psscode click on the name of the speaker on the webstie of the seminar:

Sharp L^p estimates for oscillatory integral operators of arbitrary signature

Speaker:

Marina Iliopoulou

Institution:

University of Kent, UK

Time:

Monday, October 4, 2021 - 12:00pm

Location:

Zoom

The restriction problem in harmonic analysis asks for L^p bounds on the Fourier transform of functions defined on curved surfaces. In this talk, we will present improved restriction estimates for hyperbolic paraboloids, that depend on the signature of the paraboloids. These estimates still hold, and are sharp, in the variable coefficient regime. This is joint work with Jonathan Hickman

Zoom ID is available here:

FKP meets DKP

Simon Bortz

Institution:

University of Alabama

Time:

Monday, September 27, 2021 - 12:00pm

Location:

Zoom

In the 80’s Dahlberg asked two questions regarding the $L^p$ – solvability’ of elliptic equations with variable coefficients. Dahlberg’s first question was whether $L^p$ solvability was maintained under Carleson-perturbations’ of the coefficients. This question was answered by Fefferman, Kenig and Pipher [FKP], where they also introduced new characterizations of $A_\infty$, reverse-Hölder and $A_p$ weights. These characterizations were used to create a counterexample to show their theorem was sharp.

Dahlberg’s second question was whether a Carleson gradient/oscillation condition (the DKP condition’) was enough to imply $L^p$ solvability for some p > 1. This was answered by Kenig and Pipher [KP] and refined by Dindos, Petermichl and Pipher [DPP] (in the small constant’ case). These $L^p$ solvability results can be interpreted in terms of a reverse Hölder condition for the elliptic kernel and therefore connected with the $A_\infty$ condition. In this talk, we discuss L^p solvability for a class of coefficients that satisfies a weak DKP condition’. In particular, we connect the (weak) DKP condition to the characterization of $A_\infty$ in [FKP]. This allows us to treat the large’, `small’ and ‘vanishing’ (weak) DKP conditions simultaneously and independently from the works [KP] and [DPP].

This is joint work with my co-authors Egert, Saari, Toro and Zhao. A proof of the main estimate will be sketched, but technical details will be avoided.