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DTSTART;TZID=America/New_York:20260204T130000
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SUMMARY:CMSA Q&A Seminar: Ludmil Katzarkov\, University of Miami
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Ludmil Katzarkov\, University of Miami \nTitle: New Birational Invariants \nAbstract: We will introduce the origins of the main ideas of the theory of atoms. Applications follow. Equivariant and mixed atoms will be considered.
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_2426/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-2.4.2026.docx-1-scaled.png
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DTSTART;TZID=America/New_York:20260204T140000
DTEND;TZID=America/New_York:20260204T150000
DTSTAMP:20260419T222501
CREATED:20250128T214750Z
LAST-MODIFIED:20260126T163315Z
UID:10003708-1770213600-1770217200@cmsa.fas.harvard.edu
SUMMARY:Automated Theory Formation and Interestingness in Mathematics
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: George Tsoukalas\, UT Austin Dept. of Computer Science and Google DeepMind. \nTitle: Automated Theory Formation and Interestingness in Mathematics \nAbstract: Advances in modern learning systems are beginning to demonstrate utility for select problems in research mathematics. A broader challenge is that of developing new theories automatically. This area has a rich history\, and is tied to some of the earliest work in AI. In particular\, a central question in this study was measuring the “interestingness” of mathematical concepts. \nIn this talk\, I will review this historical context and present our recent work on using large language models to synthesize interestingness measures that guide theory exploration in elementary number theory from scratch. I will conclude by outlining potential future research directions in this domain. \nJoint work done at UT Austin with Rahul Saha\, Amitayush Thakur\, Sabrina Reguyal\, and Swarat Chaudhuri.
URL:https://cmsa.fas.harvard.edu/event/newtech_2426/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-2.4.2026.docx-1-scaled.png
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DTSTART;TZID=America/New_York:20260204T170000
DTEND;TZID=America/New_York:20260204T180000
DTSTAMP:20260419T222501
CREATED:20250409T160357Z
LAST-MODIFIED:20260210T204515Z
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SUMMARY:Millennium Prize Problems Lecture - Barry Mazur: About the Birch and Swinnerton–Dyer Conjecture
DESCRIPTION:Date: February 4\, 2026 \nTime: 5:00–6:00 pm \nLocation: Harvard Science Center Hall C\, 1 Oxford St.\, Cambridge MA \nSpeaker: Barry Mazur\, Harvard University \nTitle: About the Birch and Swinnerton–Dyer Conjecture \nAbstract: \nIn the 1950s Bryan Birch and Peter Swinnerton–Dyer made computations that suggested a striking connection between a basic global invariant of an elliptic curve E over the field of rational numbers (namely\, the rank of its group of rational points) and certain asymptotics of its local arithmetic invariants (i.e.\, the number of its rational points over finite fields). \nThis initial observation has evolved into their conjecture. My lecture will be an introduction to the general ideas behind its ever-expanding development. \nRead more about the Birch and Swinnerton–Dyer Conjecture at the Clay Math website. \n  \nOrganizers: Martin Bridson\, Clay Mathematics Institute | Dan Freed\, Harvard University and CMSA | Mike Hopkins\, Harvard University \nBarry Mazur joined the Harvard University faculty in 1959 as a Junior Fellow in the Society of Fellows and advanced through the ranks to become the Gerhard Gade University Professor of Mathematics\, a position he has held since 1998. During his tenure at Harvard\, he has mentored 60 doctoral students and served as a pivotal figure in bridging topology and number theory\, notably through his classification of the possible torsion subgroups of elliptic curves over the rational numbers (Mazur’s torsion theorem)\, which identifies exactly 15 possible finite groups. This theorem\, detailed in his 1977 paper “Modular curves and the Eisenstein ideal\,” provided crucial insights into the Taniyama-Shimura conjecture and laid groundwork for Andrew Wiles’s 1994 proof of Fermat’s Last Theorem. \nHis broader research includes seminal works on étale homotopy theory (co-authored with Michael Artin in 1969)\, the arithmetic moduli of elliptic curves (with Nicholas M. Katz in 1985)\, and the Iwasawa main conjecture (proved with Andrew Wiles in 1984)\, as well as advancements in p-adic L-functions and the formulation of the Fontaine-Mazur conjecture on Galois representations. Mazur’s influence extends to public communication of mathematics; he has authored books like Imagining Numbers (2003)\, exploring historical perspectives on complex numbers. \nAmong his numerous honors\, Mazur received the Cole Prize in Number Theory from the American Mathematical Society in 1982\, the Chauvenet Prize in 1994 for expository writing\, the Leroy P. Steele Prize for Lifetime Achievement in 2000\, and election to the National Academy of Sciences in 1982. In 2011 (presented in 2013)\, he was awarded the National Medal of Science by President Barack Obama for his pioneering work in these fields.Most recently\, in 2022\, he received the Chern Medal from the International Mathematical Union\, recognizing his profound discoveries and mentorship. \n  \n\n                   \n\nMillennium Prize Problems Lecture Series \n 
URL:https://cmsa.fas.harvard.edu/event/clay_2426/
LOCATION:Harvard Science Center Hall D\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Millennium Prize Problems Lecture,Special Lectures
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