Harmonic Analysis Seminar
Abstract and additional information

Posted September 27, 2017

Last modified October 16, 2017

Reflection Positivity; Representation Theory meets CQFT

Moved by one week: We will give an overview over our work with K-H. Neeb on reflection positivity. We start with recalling the Osterwalder-Schrader Axioms for Constructive Quantum Field Theory and the Osterwalder-Schrader (OS) quantization. We then point out the natural generalization and discuss some examples. We then discuss reflection positive representations, in particular reflection positive 1-parameter subgroups. In the second part we discuss OS quantization related to the sphere.

Harmonic Analysis Seminar
Abstract and additional information

Posted September 27, 2017

Last modified October 16, 2017

Reflection Positivity; Representation Theory meets CQFT, part II

This is the second part of the series on Reflection positivity. Both talks are accessible for graduate students.

Harmonic Analysis Seminar
Abstract and additional information

Posted October 10, 2017

3:30 pm - 4:30 pm Lockett 285
Boris Rubin, Lousiana State University

Weighted Norm Estimates for Radon Transforms and Geometric Inequalities

We obtain sharp inequalities for the Euclidean k-plane transforms and the " j-plane to k-plane'' transforms acting in $L^p$ spaces on $R^n$ with a radial power weight. The corresponding operator norms are explicitly evaluated. The results extend to Funk-type transforms on the sphere and Grassmann manifolds. As a consequence, we obtain new weighted estimates of measures of planar sections for measurable subsets of $R^n$. The corresponding unweighted $L^p -L^q$ estimates and related open problems will be discussed.

Harmonic Analysis Seminar
Abstract and additional information

Posted November 14, 2017

3:30 pm - 4:20 pm Lockett 285
Anton Zeitlin, LSU

Enumerative geometry and quantum integrable systems

Abstract: The miraculous correspondence between 3-dimensional Gauge theory and integrable models based on quantum groups was observed by Nekrasov and Shatashvili in 2009. That discovery led to a lot of interesting developments in mathematics, in particular in enumerative geometry, bringing a new life to older ideas of Givental, and enriching it with flavors of geometric representation theory via the results of Braverman, Maulik, Okounkov and many others. In this talk I will focus on recent breakthroughs, originating from the work of Okounkov on the subject, leading to proper mathematical understanding of Nekrasov-Shatashvili original papers.

Harmonic Analysis Seminar
Abstract and additional information

Posted November 14, 2017

3:30 pm - 4:20 pm Lockett 285
Anton Zeitlin, LSU

Enumerative geometry and quantum integrable systems

Abstract: The miraculous correspondence between 3-dimensional Gauge theory and integrable models based on quantum groups was observed by Nekrasov and Shatashvili in 2009. That discovery led to a lot of interesting developments in mathematics, in particular in enumerative geometry, bringing a new life to older ideas of Givental, and enriching it with flavors of geometric representation theory via the results of Braverman, Maulik, Okounkov and many others. In this talk I will focus on recent breakthroughs, originating from the work of Okounkov on the subject, leading to proper mathematical understanding of Nekrasov-Shatashvili original papers.