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DTSTART;TZID=America/New_York:20251211T140000
DTEND;TZID=America/New_York:20251211T150000
DTSTAMP:20260510T115724
CREATED:20251202T153632Z
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UID:10003842-1765461600-1765465200@cmsa.fas.harvard.edu
SUMMARY:Covers of curves\, Ceresa cycles\, and unlikely intersections
DESCRIPTION:Algebra Seminar \nSpeaker: Padamavathi Srinivasan\, Boston University \nTitle: Covers of curves\, Ceresa cycles\, and unlikely intersections \nAbstract: The Ceresa cycle is a canonical homologically trivial algebraic cycle associated to a curve in its Jacobian. In his 1983 thesis\, Ceresa showed that this cycle is algebraically nontrivial for a very general complex curve of genus at least 3. In the last few years\, there have been many new results shedding light on the locus in the moduli space of genus g curves where the Ceresa cycle becomes torsion. We will survey these recent results and provide new examples of positive dimensional families of curves where only finitely many members of the family have torsion Ceresa cycle. The main idea is to study covers of curves with many automorphisms\, and we will explain how we use the covering maps together with results on unlikely intersections in abelian varieties to construct such families. This is joint work with Tejasi Bhatnagar\, Sheela Devadas and Toren D’Nelly Warady. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_121125/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-12.11.25.docx-scaled.png
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DTSTART;TZID=America/New_York:20251216T140000
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CREATED:20251210T174651Z
LAST-MODIFIED:20251211T144851Z
UID:10003845-1765893600-1765897200@cmsa.fas.harvard.edu
SUMMARY:Electrical networks\, Grassmannians\, and cluster algebras
DESCRIPTION:Algebra Seminar \nSpeaker: Lazar Guterman\, Hebrew University of Jerusalem \nTitle: Electrical networks\, Grassmannians\, and cluster algebras \nAbstract: An electrical network with $n$ boundary vertices induces a matrix called the response matrix which measures the electrical properties of the network. The set of response matrices of all electrical networks has a characterization in terms of positivity of circular minors. Alman\, Lian and Tran constructed a cluster algebra on the set of circular minors\, which encodes the tests for positivity of these minors. Lam established the embedding of the set of electrical networks with $n$ boundary vertices into the totally nonnegative Grassmannian $Gr_{\ge0}(n-1\,2n)$. The coordinate ring of the Grassmannian has a cluster algebra structure as was proved by Scott. Given an electrical network\, we find a relation between circular minors of its response matrix and Plücker coordinates of its image in the Grassmannian. Using this property\, we prove that for an odd $n$ the two cluster algebras\, on circular minors and on the Grassmanian\, become isomorphic after a natural freezing and subsequent trivialization of certain variables in their initial seeds. We apply this isomorphism in order to relate the tests for positivity of circular minors to tests for positivity in the Grassmannian. The talk is based on a joint work with Boris Bychkov and Anton Kazakov. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_121625/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-12.16.25.docx-scaled.png
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