Bruno Klingler, Humboldt Universitaet Berlino
Tame topology and algebraic geometry
Lunedì 11 Marzo 2019, ore 16:30 precise
Aula Seminari 6 piano, Ed. La Nave | |
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Anton Baranov, Saint Petersburg State University
Spectral synthesis for systems of exponentials and reproducing kernels
Giovedì 07 Febbraio 2019, ore 16:00
Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50, Milano | |
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Guido Kings, Università di Regensburg
The Birch-Swinnerton-Dyer conjecture, some recent progress
Lunedì 07 Gennaio 2019, ore 16:00
Aula C, Dipartimento di Matematica, Via C. Saldini 50, Milano | |
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Arkady Tsinober, Tel Aviv University
Turbulence versus Mathematics and vice versa
Martedì 04 Dicembre 2018, ore 16:00
Aula 3015 del Dipartimento di Matematica e Applicazioni dell'Università di Milano - Bicocca | |
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Shigefumi Mori, Kyoto University Institute of Advanced Study
BIRATIONAL EQUIVALENCE OF ALGEBRAIC VARIETIES
Lunedì 26 Novembre 2018, ore 16:30
Aula Chisini, Diparimento di Matematica, Via C. Saldini 50 | |
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Terence Tao, University of California, Los Angeles
VAPORIZING AND FREEZING THE RIEMANN ZETA FUNCTION
Venerdì 22 Giugno 2018, ore 14:30
Edificio U4, P.zza della Scienza, 4, Aula Luisella Sironi |
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Abstract
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In 1950, de Bruijn studied the effect of evolving the Riemann zeta function (or more precisely, a closely related function known as the Riemann xi function) by the (backwards) heat equation. His analysis, together with later work by Newman, showed that there existed a finite constant Lambda, at most 1/2 in value, such that the Riemann hypothesis for this evolved function was true at times greater than or equal to Lambda, and false below that threshold. Thus the Riemann hypothesis for the zeta function is equivalent to Lambda being non-positive. Recently, in joint work with Brad Rodgers, I was able to establish the complementary estimate that Lambda is non-negative, confirming a conjecture of Newman; thus, the Riemann hypothesis for zeta, if true, is only "barely so". The proof relies on an analysis of the dynamics of zeroes of entire functions under heat flow; it turns out that as one evolves forward in time, the zeroes "freeze" into approximate arithmetic progressions, while if one evolves backwards, the zeroes "vaporize" to leave the critical line. In followup work in an online collaborative "Polymath" project, the upper bound on Lambda has also been improved. We describe these results and their proofs in this talk.
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