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PRODID:Mathematics Seminar Calendar
BEGIN:VEVENT
UID:20211025T141648-29107@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:The dual Lagrangian fibration of compact hyper-Kahler manifolds
DESCRIPTION:Speaker\: Yoonjoo Kim, Stony Brook University\r\nA compact hyper-Kahler manifold is a higher dimensional generalization of a K3 surface. An elliptic fibration of a K3 surface correspondingly generalizes into the so-called Lagrangian fibration of a compact hyper-Kahler manifold. It is known that an elliptic fibration of a K3 surface is always "self-dual" in a certain sense. This turns out to be not the case for higher-dimensional Lagrangian fibrations. In this talk, we will explicitly construct the dual of Lagrangian fibrations of all currently known examples of compact hyper-Kahler manifolds.\r\n\r\nPasscode: MSUALG
LOCATION:Online (virtual meeting)
DTSTART:20210915T200000Z
DTEND:20210915T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29107
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BEGIN:VEVENT
UID:20211025T141648-29138@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:Abelian varieties with given p-torsion representation
DESCRIPTION:Speaker\: Shiva Chidambaram, MIT\r\nThe Siegel modular variety $\mathcal{A}_2(3)$, which parametrizes abelian surfaces with full level $3$ structure, was recently shown to be rational over $\mathbf{Q}$ by Bruin and Nasserden. What can we say about its twist $\mathcal{A}_2(\rho)$ that parametrizes abelian surfaces $A$ whose $3$-torsion representation is isomorphic to a given representation $\rho$? While it is not rational in general, it is always unirational over $\mathbf{Q}$ showing that $\rho$ arises as the $3$-torsion representation of infinitely many abelian surfaces. We will discuss how we can obtain an explicit description of the universal object over such a unirational cover of $\mathcal{A}_2(\rho)$ using invariant theoretic ideas, thus parametrizing families of abelian surfaces with fixed $3$-torsion representation. Similar ideas work in a few other cases, showing in particular that whenever $(g,p) = (1,2)$, $(1,3)$, $(1,5)$, $(2,2)$, $(2,3)$ and $(3,2)$, the necessary condition of cyclotomic similitude is also sufficient for a mod $p$ Galois representation to arise from the $p$-torsion of a $g$-dimensional abelian variety.
LOCATION:Online (virtual meeting)
DTSTART:20211006T200000Z
DTEND:20211006T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29138
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BEGIN:VEVENT
UID:20211025T141648-29147@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:Rigidity in contact topology
DESCRIPTION:Speaker\: Honghao Gao, MSU\r\nLegendrian links play a central role in low dimensional contact topology. A rigid theory uses invariants constructed via algebraic tools to distinguish Legendrian links. The most influential and powerful invariant is the Chekanov-Eliashberg differential graded algebra (Chekanov, Inventiones, 2002), which set apart the first non-classical Legendrian pair and stimulated many subsequent developments. The functor of points for the dga is a moduli space which acquires rich algebraic structures and can distinguish exact Lagrangian fillings. Such fillings are difficult to construct and to study, whereas the only known classification is the unique filling for Legendrian unknot (Eliashberg-Polterovich, Annals, 1996). For a long time, a folklore belief is that exact Lagrangian fillings are scarce and a Legendrian link can only have finitely many, based on the observation from limited examples.\r\n\r\n\r\n\r\nIn this talk, I will report a joint work with Roger Casals, where we applied the techniques from contact topology, microlocal sheaf theory and cluster algebras, and successfully found the first examples of Legendrian links with infinitely many Lagrangian fillings, reversing the general belief.
LOCATION:Online (virtual meeting)
DTSTART:20211013T200000Z
DTEND:20211013T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29147
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BEGIN:VEVENT
UID:20211025T141648-29126@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:Rational maps from products of curves
DESCRIPTION:Speaker\: Olivier Martin, Stony Brook University\r\nI will present recent joint work with N. Chen about dominant rational maps from products of curves to surfaces with p_g=q=0. The gonality of an algebraic curve C is the minimal degree of a non-constant morphism from C to the projective line. Our main result is that under some assumptions the minimal degree of a dominant rational map from a product of two curves to a surface with p_g=q=0 is the product of their gonalities. In particular, a product of hyperelliptic curves of general type does not admit dominant rational maps of degree less than 4 to P^2. I will finish by presenting open problems and some strategies to attack them.
LOCATION:Online (virtual meeting)
DTSTART:20211020T200000Z
DTEND:20211020T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29126
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BEGIN:VEVENT
UID:20211025T141648-29127@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:Chow groups of Severi--Brauer varieties and biquaternion algebras
DESCRIPTION:Speaker\: Eoin Mackall, University of Maryland\r\nThe Chow groups of Severi--Brauer varieties associated to biquaternion division algebras were originally computed by Karpenko in the mid nineties. The main difficulty in these computations is determining whether or not CH^2, the group of codimension 2 cycles, contains nontrivial torsion; for these varieties this group is torsion-free. Since his original proof, Karpenko has given two other proofs of this result. All of these proofs involve some clever use of K-theory to determine relations between some explicit cycles. In this talk, I'll discuss a new geometric method that one can use to determine these same relations. Passcode: MSUALG
LOCATION:Online (virtual meeting)
DTSTART:20211027T200000Z
DTEND:20211027T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29127
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BEGIN:VEVENT
UID:20211025T141648-29143@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Karl Schwede, University of Utah\r\n
LOCATION:C304 Wells Hall
DTSTART:20211103T200000Z
DTEND:20211103T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29143
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BEGIN:VEVENT
UID:20211025T141648-29128@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Rong Zhou, Cambridge\r\n
LOCATION:Online (virtual meeting)
DTSTART:20211110T210000Z
DTEND:20211110T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29128
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BEGIN:VEVENT
UID:20211025T141648-29121@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Katrina Honigs, Simon Fraser University\r\n
LOCATION:Online (virtual meeting)
DTSTART:20211117T210000Z
DTEND:20211117T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29121
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BEGIN:VEVENT
UID:20211025T141648-29109@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Jack Petok, Dartmouth\r\nTBA
LOCATION:Online (virtual meeting)
DTSTART:20211201T210000Z
DTEND:20211201T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29109
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BEGIN:VEVENT
UID:20211025T141648-29116@math.msu.edu
DTSTAMP:20211025T141648Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Salim Tayou, Harvard University\r\n
LOCATION:C304 Wells Hall
DTSTART:20211208T210000Z
DTEND:20211208T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29116
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