DIFFERENTIAL GEOMETRY
March 23, 2021 9:00 pmI will present work on establishing the correspondence between the (appropriately defined) Hodge numbers of the moduli spaces of parabolic Higgs bundles for the structure groups SL_n and PGL_n, building...
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DIFFERENTIAL GEOMETRY
March 16, 2021 9:00 pmIn this talk, I will discuss some structural results for the cohomology of the moduli of semi-stable SL_n Higgs bundles on a curve. One consequence is a new proof of the...
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DIFFERENTIAL GEOMETRY
March 9, 2021 8:00 pmFor convex complete intersections, the Gromov-Witten (GW) invariants are often computed using the Quantum Lefshetz Hyperplane theorem, which relates the invariants to those of the ambient space. However, even in...
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DIFFERENTIAL GEOMETRY
March 2, 2021 8:00 amA disc potential function plays an important role in studying a symplectic manifold and its Lagrangian submanifolds. In this talk, I will explain how to compute the disc potential function of...
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DIFFERENTIAL GEOMETRY
November 24, 2020 8:00 pmOne possible interpretation of the SYZ conjecture is that for a polarized family of CY manifolds near the large complex structure limit, there is a special Lagrangian fibration on the...
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DIFFERENTIAL GEOMETRY
November 17, 2020 8:00 pmI will discuss the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibration structure, when the Kahler class degenerates to...
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DIFFERENTIAL GEOMETRY
November 10, 2020 8:00 pmThe 2D Toda system consists of a complicated set of infinitely many coupled PDEs in infinitely many variables that is known to assemble into an infinite-dimensional integrable system. Krichever and...
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DIFFERENTIAL GEOMETRY
October 27, 2020 8:00 amThe derived category of a Fano threefold Y of Picard rank 1 and index 2 admits a semiorthogonal decomposition. This defines a non-trivial subcategory Ku(Y) called the Kuznetsov component, which...
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DIFFERENTIAL GEOMETRY
October 20, 2020 8:00 pmWhen we upgrade from equivariant cohomology to equivariant K-theory, many important algebraic/geometric tools such as dimensional vanishing become inapplicable in general. I will explain some nice conditions we can impose on K-theory...
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DIFFERENTIAL GEOMETRY
October 13, 2020 8:00 pmQuiver theory and machine learning share a common ground, namely, they both concern about linear representations of directed graphs. The main difference arises from the crucial use of non-linearity in...
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