"Reason is immortal, all else mortal." - Pythagoras
Spring 2022
Organized by Polona Durcik, Mario Stipčić, and Mihaela B. Vajiac, sponsored by CECHA.
The talks will be held in a hybrid format, on Zoom (meeting ID: 99396752824) and/or on campus at Keck Center of Science and Technology (no. 30 on the Campus map, at the intersection of Walnut Ave and Center St), room KC 156.
Schedule
Friday, February 18, 2:30pm - 3:30pm
Ahmed Sebbar (Chapman University)
On a question of J. P. Serre, Part I
Friday, February 25, 2:30pm - 3:30pm
Michel Balazard (Institut de Mathématiques de Marseille)
The criteria of Nyman and Baez-Duarte for the Riemann hypothesis
In his doctoral dissertation, Nyman gave in 1950 a necessary and sufficient criterion for the validity of the Riemann hypothesis, in terms of the density of some subspace in L^2(0,1). In 2003, Baez-Duarte gave a modified form of this criterion. The talk will present these two criteria, as well as related results and questions.
Friday, March 4, 2:30pm - 3:30pm
Ahmed Sebbar (Chapman University)
On a question of J. P. Serre, Part II
Friday, March 11, 2:30pm - 3:30pm
Daniel Alpay (Chapman University)
Discrete analytic functions and Schur analysis
We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation problem. We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers. The talk is based on collaborations with F. Colombo, K. Diki, I. Sabadini and D. Volok.
Friday, March 18, 2:30pm - 3:30pm
Brett Wick (Washington University in St. Louis)
Commutators of Calderón-Zygmund Operators and Bounded Mean Oscillation (or Factorization and Hardy Spaces)
Calderón-Zygmund operators play an important role in partial differential equations and complex analysis. Some problems in analysis benefit from an understanding of the commutation between certain operators or the factorization of functions from natural function spaces. These topics all interact when studying the commutators of Calderón-Zygmund operators and multiplication operators. In this talk, we will discuss some recent results about commutators of certain Calderón-Zygmund operators and BMO spaces and how these generate bounded operators on Lebesgue spaces. Motivations and connections to operator theory and partial differential equations will be provided. Versions of these results on the Heisenberg group, pseudoconvex domains with $C^2$ boundary, and other examples will be explained to show how the general theory carries over to many other settings. This talk is based on joint collaborative work.
Friday, April 22, 2pm - 3pm
Oumar Wone (Chapman University)
Abel ordinary differential equation and projective connections
We give some first integrals of Abel ordinary differential equation by making use of projective connections.
Friday, April 29, 2pm - 3pm
José Ramón Madrid Padilla (UCLA)
On classical inequalities for autocorrelations and autoconvolutions
We will discuss some convolution inequalities on the real line, the study of these problems is motivated by a classical problem in additive combinatorics about estimating the size of Sidon sets. We will also discuss many related open problems. This talk will be accessible for a broad audience.
Friday, May 6, 2pm - 3pm
Antonino De Martino (Politecnico di Milano)
The F-resolvent equation and Riesz projectors for the F-functional calculus
The Fueter-Sce-Qian mapping theorem is a two steps procedure to extend holomorphic functions of one complex variable to quaternionic or Clifford algebra-valued functions in the kernel of a suitable generalized Cauchy-Riemann operator. Using the Cauchy formula of slice monogenic functions it is possible to give the Fueter-Sce-Qian extension theorem an integral form and to define the F-functional calculus for n-tuples of commuting operators. This functional calculus is defined on the S-spectrum but it generates a monogenic functional calculus in the spirit of McIntosh and collaborators. In this talk the aim to show that the F-functional calculus generates the Riesz projectors via the so-called F-resolvent equation in the Clifford algebra setting. (joint work with F.Colombo, I.Sabadini)