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Title: Topics in computers and mathematics

Abstract: Advances in computation and machine learning are changing the way we do pure mathematics and theoretical physics. Using examples from differential geometry, finite group theory and other fields, I will survey some directions which I believe will have major impact during the coming decade: machine learning, ML inspired numerical methods, computer assisted proofs and interactive theorem proving.

Registration is required to receive the Zoom information.

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TBD

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

TITLE: Nonlinear stability of Kerr black holes for small angular momentum

ABSTRACT: According to a well-known conjecture,   initial data sets,  for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $|a|/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon)   which approaches  (globally)  a nearby Kerr solution.
I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum, i.e. $, $|a|/m $ sufficiently small. The work, ArXiv:2104.11857v1,  also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr,  with Szeftel and Elena Giorgi,  which I will also describe.
Talk char: Lydia Bieri

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In solidarity with Azat Miftakhov

*Starting at 4pm Central European Summer Time (UTC+2)*

It will be organized online by the Azat Miftakhov committee in solidarity with Azat Miftakhov, a graduate student from Moscow State University who has been arbitrarily detained by Russian state authorities for almost two years and a half.

4:00 pm Cédric Villani (Member of the French National Assembly)
Opening speech

4:15 pm Maryna Viazovska (École Polytechnique Fédérale de Lausanne, Switzerland)
tba

5:15 pm Alexander Bufetov (CNRS & Institut de Mathématiques de Marseille, France & Steklov, IITP RAS, Russia)
Determinantal point processes: quasi-symmetries, minimality and interpolation

6:15 pm Peter Scholze (Universität Bonn, Germany)
Condensed Mathematics

* Tokyo at 11pm, Moscow at 5pm, Bonn, Paris and Warsaw at 4pm, London at 3pm, New York at 10am, San Francisco at 7am

The webinar will be broadcast live on several websites whose
addresses will be announced a few days before. Further
the information available at caseazatmiftakhov.org

I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

Zoom: https://harvard.zoom.us/j/977347126

Taxanes act by stabilizing microtubules (MTs) and prolong survival in men with prostate cancer (PCa), but biomarkers predictive of responses and clinically actionable mechanism(s) of resistance have yet to be identified. We recently reported that a decrease or absence of MT bundling, despite high levels of intratumoral taxanes, is a basis and a potential pharmacodynamic biomarker of taxane resistance. To determine the molecular basis for this impaired MT bundling, we treated docetaxel sensitive PCa models in vivo for multiple cycles until resistance, and found upregulation of FOXJ1 (a master transcription factor regulating tubulin associated proteins), as well as one of its downstream effector protein, TPPP3, in the resistant tumors. Moreover, mining of patient databases showed that amplification of the FOXJ1 gene is also associated with taxane exposure. Together these data implicate the FOXJ1-TPPP3 regulatory network in taxane resistance. In parallel with these in vivo studies, we have carried in vitro drug screens for agents that enhance responses to docetaxel in 3D/organoid culture. A prominent agent that emerged is a histone methyltransferase inhibitor. Our overall goals are to identify clinically meaningful mechanisms of taxane resistance, to develop therapeutic combinations that enhance efficacy and/or target these resistance mechanisms, and to identify biomarkers indicative of specific mechanisms. Our hypotheses, which are based on our published and preliminary data, are that one major mechanism for taxane resistance is upregulation of the FOXJ1-TPPP3 pathway, and that combination therapies can be developed that enhance taxane efficacy and delay or prevent the emergence of resistance. The specific aims are 1) Determine the effect of FOXJ1-TPPP3 regulatory network on microtubule dynamics, stability and target-engagement by taxanes in vitro and in vivo and 2) Identify effective combination therapies to enhance docetaxel responses and overcome taxane resistance.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)

Zoom: https://harvard.zoom.us/j/977347126