2017: An Overview of Wavelet Theory, With an eye on Superoscillations
Lectures by Professor David Walnut, George Mason University

SCHEDULE:
November 6th from 4 p.m. to 5:30 p.m.
Lecture 1: Some Time-Frequency Transforms

• What is a Time-Frequency distribution/representation?
• The Short-Time Fourier Transform
• The Ambiguity Function and Wigner's Distribution
• Uncertainty Principles

November 7th from 4 p.m. to 5:30 p.m.
Lecture 2: Gabor Theory

• D. Gabor's notion of information area
• Discretizing the Short-Time Fourier Transform
• Stability in time-frequency representations
• The Balian-Low Theorem
• The Amalgam BLT (Heil)
• The Zak transform and proofs.

November 8th from 4 p.m. to 7 p.m.
Lecture 3: Theory of Frames

• Finite Frames
• Abstract Frames
• The Frame operator
• Riesz bases
• Some historical remarks
• The BLT from the perspective of frames

Lecture 4: Structure Theorems for Gabor Frames

• Existence of Gabor frames
• Zak transform methods
• Density theorems for Gabor frames
• The Wexler-Raz and Ron-Shen duality
• Wilson bases

Lecture 5: Continuous and Discrete Wavelets

• The Continuous Wavelet transform of Grossman and Morlet
• The CWT as a time-frequency (time-scale) transformation
• Relation to the Calderon Reproducing Formula
• Discrete Wavelet decompositions of Frazier and Jawerth
• Relation to Littlewood-Paley theory

November 9th from 4 p.m. to 7 p.m.
Lecture 6: Orthonormal Bases of Wavelets

• The Haar Wavelet basis
• The Shannon Wavelet basis
• The Meyer Wavelet basis
• Local Cosine bases (Coifman-Weiss)
• Wavelet Sets (Weiss et. al)

Lecture 7: Multiresolution Analysis (Mallat-Meyer)

• Definition of MRA in one dimension
• Finding the wavelet from the scaling function
• The Daubechies wavelets
• MRA in higher dimensions

Lecture 8: Coorbit Spaces (Feichtinger-Grochenig)

• Representations of the Heisenberg group and the Affine group
• Co-orbit spaces from irreducible group representations
• Co-orbit spaces as reproducing kernel Hilbert spaces
• Frames and sampling in co-orbit spaces

November 10th from 2 p.m. to 3 p.m.
Lecture 9: Wavelets in Functional Analysis

• Modulation spaces
• The Feichtinger Algebra
• Pseudodifferential operators and Gabor frames
• Wavelets as unconditional bases for Banach spaces
• Wavelets and operators

About Professor David Walnut:
David F. Walnut received his Ph.D. degree in mathematics from the University of Maryland, USA in 1989 under the direction of John Benedetto. He has been on the faculty at George Mason University in Fairfax, Virginia, USA since 1990, where he currently holds the rank of Professor. His mathematical interests include Euclidean harmonic analysis, time-frequency analysis and sampling theory.

2017: Mathematics, Signal Processing and Linear Systems: New Problems and Directions

The main topics of the conference were the intersection between mathematical analysis (in a wide sense), signal processing, and applications to electrical engineering problems. The research presented here is at the crossroad of mathematics (in particular complex analysis, functional analysis, and stochastic processes), the theory of linear systems, signal processing, and electrical engineering. 

Organizers:

• Dr. Daniel Alpay, Foster G. and Mary McGaw Professorship in Mathematical Sciences, email: alpay@chapman.edu
• Dr. Mihaela B. Vajiac, Associate Professor of Mathematics, Director of CECHA, email: mbvajiac@chapman.edu

2016: The “International Conference on Complex Analysis and Operator Theory - Celebrating Daniel Alpay’s 60th birthday” took place at Chapman University, Orange, California, November 4-7, 2016.

The main topics of the conference were complex analysis, operator theory and other areas of mathematics which have been touched by Professor Daniel Alpay during his fertile scientific activity. This meeting was the perfect occasion to celebrate his 60th birthday among friends and collaborators.

• Scientific: F. Colombo, D.C. Struppa, M.B. Vajiac, A. Vajiac
• Organizing: I. Sabadini, M.B. Vajiac

List of speakers: J. Behrndt, V. Bolotnikov, F. Colombo, J. Gantner, W. Helton, T. Hempfling, P. Jorgensen, H.T. Kaptanoglu, E. Kvaalen, D. Levanony, I. Lewkovicz, M. Mboup, A. Pinhas, I. Sabadini, B. Schneider, A. Sebbar, D.C. Struppa, M.B. Vajiac, A. Vajiac, D. Volok, A. Yger

Schedule of events

Book of Abstracts

2016: Series of 12 lectures on Operators of Infinite Order and Exact WKB Analysis, Professor Takashi Aoki, Kindai University

Von Neumann Hall (545 W Palm), 9-11 a.m., August 22-26 and August 29th.

Part I Differential operators, microdifferential operators and pseudodifferential operators of infinite order

1. Introduction
2. Algebraic definitions of pseudodifferential operators in complex analytic category
3. Kernel functions
4. Symbols of pseudodifferential operators and symbolic calculus
5. Exponential calculus
6. Applications

Part II Exact WKB analysis

1. Introduction
2. WKB solutions of ODE of second order with a large parameter
3. Borel sums of WKB solutions and connection formulas
4. WKB solutions and microdifferential operators
5. Higher-order equations and infinite-order equations
6. Applications to special functions

2014: Workshop on Integral transforms, boundary values and generalized functions

Continuing the tradition established in the past two years, the Center of Excellence in Complex and Hypercomplex Analysis (CECHA) at Chapman University organized the Workshop during the period of October 17th to October 21st, 2014 "Integral transforms, boundary values and generalized functions".

The Organizing Committee and members of the CECHA:

• Daniele C. Struppa
  Email: struppa@chapman.edu
• Mihaela Vajiac
  Email: mbvajiac@chapman.edu
• Irene Sabadini
  Email: i.sabadini@alice.it

Schedule of the events and talks.

List of speakers: D. C. Struppa, M.B. Vajiac, A. Vajiac, D. Alpay, M. Martin, P. Cerejeiras?, D. Clahane, I. Sabadini, F. Colombo, G. Gentili, U. Kahler, M. Libine, C. Nolder, L. Cnudde, M. Shapiro, ?M.E. Luna-Elizarraras, A. Sebbar.

2013: Workshop on Results in Mathematics and Physics obtained by Methods of Hypercomplex Analysis

The Center of Excellence in Complex and Hypercomplex Analysis (CECHA) at Chapman University organized a Workshop during the period of November 7th 2013 to November 11th 2013, with the topic: "Results in Mathematics and Physics obtained by Methods of Hypercomplex Analysis".

Schedule of Events

The Organizing Committee and members of the CECHA:

• Daniele C. Struppa
  Email: struppa@chapman.edu
• Mihaela Vajiac
  Email: mbvajiac@chapman.edu
• Adrian Vajiac
  Email: avajiac@chapman.edu
• Maria Elena Luna Elizarraras
  Email: eluna@esfm.ipn.mx
• Michael Shapiro
  Email: shapiro@esfm.ipn.mx

List of confirmed speakers:Daniele C. Struppa, Mihaela Vajiac, Adrian Vajiac, Maria Elena Luna Elizarraras, Michael Shapiro, Daniel Alpay, Craig Nolder, Irene Sabadini, Fabrizio Colombo, Graziano Gentili, Joao Morais, Matvei Libine, Thomas Hempfling, Dominic Rochon, Lander Cnudde?.

2012: Workshop on Function Theories for Bicomplex and Hyperbolic Numbers

The Center of Excellence in Complex and Hypercomplex Analysis (CECHA) at Chapman University organized the workshop entitled Function Theories for Bicomplex and Hyperbolic Numbers, which took place at Chapman University, October 22-26, 2012, in the Sandhu Conference Center.

Function Theories for Bicomplex and Hyperbolic numbers have recently gained momentum in the Mathematics and Physics communities. The goal of this workshop has been to provide and stimulate interaction and communication among the researchers whose scientific interests include these two areas of Mathematics.

The talks and discussions were directly related to the Analysis of Bicomplex and Hyperbolic Numbers and their applications.

The Organizing Committee and members of the CECHA:

• Daniele C. Struppa
  Email: struppa@chapman.edu
• Adrian Vajiac
  Email: avajiac@chapman.edu
• Mihaela Vajiac
  Email: mbvajiac@chapman.edu
• Maria Elena Luna Elizarraras
  Email: eluna@esfm.ipn.mx
• Michael Shapiro
  Email: shapiro@esfm.ipn.mx

List of confirmed participants:Daniele C. Struppa, Adrian Vajiac, Mihaela Vajiac, Maria Elena Luna Elizarraras, Michael Shapiro, John Ryan, Dominic Rochon, Daniel Alpay, Franciscus Sommen, Uwe Kahler, Paula Cerejeiras, Matvei Libine, Sebastien Tremblay, Craig Nolder, Irene Sabadini, Fabrizio Colombo, Dana Clahane