Speaker: Yiannis Sakellaridis (Rutgers Newark and IAS) -

Abstract: I will introduce a new paradigm for comparing relative trace formulas,

in order to prove instances of (relative) functoriality and relations

between periods of automorphic forms.

More precisely, for a spherical variety X=H\G of rank one, I will prove

that there is an explicit "transfer operator" which transforms the

orbital integrals of the relative trace formula for X x X/G to the

orbital integrals of the Kuznetsov formula for GL(2) or SL(2), equipped

with suitable non-standard test functions. The operator is determined by

the L-value associated to the square of the H-period integral, and the

proof uses a deep theory of Friedrich Knop on the cotangent bundles of

spherical varieties. This is part of an ongoing joint project with

Daniel Johnstone and Rahul Krishna, who are proving instances of the

fundamental lemma. Globally, this transfer will induce an identity of

relative trace formulas and global relative characters, translating to

an Ichino–Ikeda type formula that relates the square of the H-period to

the said L-value.

This can be viewed as part of the program of relative functoriality, a

generalization of the Langlands functoriality conjecture, predicting

relations between the automorphic spectra of two spherical varieties

when there is a map between their dual groups. The case under

consideration here is the simplest non-abelian case of this, when the

dual groups are equal and of rank one. If time permits, I will discuss

how the transfer operator here and in a few examples of higher rank

where it is known is a "deformation" of an abelian transfer operator

obtained by replacing the spherical variety by its asymptotic cone (or

boundary degeneration).

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Speaker: Siming He (University of Maryland) -

Abstract: http://www.terpconnect.umd.edu/~lvrmr/2017-2018-F/Classes/RIT.shtml

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Speaker: Mert Gurbuzbalaban (Rutgers University) - https://mert.lids.mit.edu

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Speaker: Kasso Okoudjou (UMD) -

Abstract: I will describe a recent construction of multivariate Wilson orthonormal basis, that generalizes many of the existing ones.

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Speaker: Dipendra Prasad (UMD and TIFR (India)) - http://www.math.tifr.res.in/~dprasad/

Abstract: Following the natural instinct that when a group operates on a number

field then every term in the class number formula should factorize ‘compatibly’ ac-

cording to the representation theory (both complex and modular) of the group, we are

led — in the spirit of Herbrand-Ribet’s theorem on the p-component of the class num-

ber of Q(\zeta_p) — to some natural questions about the p-part of the classgroup of any CM

Galois extension of Q as a module for Gal(K/Q), and about integrality of L-values.

This talk will attempt doing this in terms of precise conjectures. Talk is based on a recent paper

with the same title available in the arXiv.

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Speaker: Prof. Jeff Calder (School of Mathematics, University of Minnesota) - http://www-users.math.umn.edu/~jwcalder/

Abstract: Semi-supervised learning refers to machine learning algorithms that make use of both labeled data and unlabeled data for learning tasks. Examples include problems such as speech recognition, website classification, and discovering folding structure of proteins. In many problems there is an abundance of unlabeled data, while labeled data often requires expert labeling and is expensive to obtain. This has led to a resurgence of semi-supervised learning techniques, which use the topological or geometric properties of large amounts of unlabeled data to aid the learning task. In this talk, I will discuss some new rigorous PDE scaling limits for existing semisupervised learning algorithms and their practical implications. I will also discuss how these scaling limits suggest new ideas for fast algorithms for semi-supervised learning.

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Speaker: Adam Kanigowski

http://www.adkanigowski.cba.pl/en.php

Abstract: Parabolic dynamical systems are systems of intermediate (polynomial) orbit growth. Most important classes of parabolic systems are: unipotent flows on homogeneous spaces and their smooth time changes, smooth flows on compact surfaces, translation flows and IET's (interval exchange transformations). Since the entropy of parabolic systems is zero, other properties describing chaoticity are crucial: mixing, higher order mixing, decay of correlations.

One of the most important tools in parabolic dynamics is the Ratner property (on parabolic divergence), introduced by M. Ratner in the class of horocycle flows. This property was crucial in proving famous Ratner's rigidity theorems in the above class.

We will introduce generalisations of Ratner's property for other parabolic systems and discuss it's consequences for chaotic properties. In particular this allows to approach the Rokhlin problem in the class of smooth flows on surfaces and in the class of smooth time changes of Heisenberg nilflows.

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Speaker: Yannis Kevrekidis (Chem and Biomolec Eng. and Applied Math and Stat, Johns Hopkins)

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Speaker: Behrang Forghani (University of Connecticut) - https://sites.google.com/site/behrangforghani/

Abstract: TBA

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Speaker: Fei Lu (John Hopkins University) - http://www.math.jhu.edu/~feilu/

Abstract: The need to develop reduced nonlinear statistical-dynamical models from time series of partial observations of complex systems arises in many applications such as geophysics, biology and engineering. The challenges come mainly from memory effects due to the nonlinear interactions between resolved and unresolved scales, and from the difficulty in inference from discrete data.

We address these challenges by introducing a discrete-time stochastic parametrization framework, in which we infer nonlinear autoregression moving average (NARMA) type models to take the memory effects into account. We show by examples that the NARMA type stochastic reduced models that can capture the key statistical and dynamical properties, and therefore can improve the performance of ensemble prediction in data assimilation. The examples include the Lorenz 96 system (which is a simplified model of the atmosphere) and the Kuramoto-Sivashinsky equation of spatiotemporally chaotic dynamics.

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Speaker: Matthew Yu (UMD) -

Abstract: We will introduce the concept of a topological field theory, namely Chern-Simons theory, and describe show how some results of the quantum Hall effect can be derived from the Chern-Simons action. I will be following Tong with some additional remarks on topological field theories.

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Speaker: Abram Kagan (UMCP) -

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