Monday, November 16th, 2026
Math Event: Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: - No talk
Time: 12:30 PM - 1:55 PM
Location:
Speaker:
Abstract: No seminar due to the SCGP Workshop https://scgp.stonybrook.edu/archives/47253
Speaker:
Abstract: No seminar due to the SCGP Workshop https://scgp.stonybrook.edu/archives/47253
Math Event: Algebraic Geometry Seminar: Shigeru Mukai - Toward an action of Conway group Co_p on a symplectic variety in characteristic p = 2, 3
Time: 4:00 PM - 5:00 PM
Location:
Speaker: Shigeru Mukai
Abstract: Only three finite simple groups can act on a K3 surface bi-holomorphically: A_5, A_6 and L_2(7). Bigger ones can act in the following variations:\r\n • K3 surfaces over a field of positive characteristic p > 0,\r\n • holomorphic symplectic manifolds of type K3^[n] and OG10, and\r\n • (= 1+2) symplectic manifolds in positive characteristic.\r\nFor example, the alternating group A_7 act birationally in the case both 1 and 2. The most interesting but still conjectural is the case 3. Sporadic groups Higman-Sims (HS), McLaughlin (McL) and two Conway groups (Co_2 and Co_3) are expected to have a birational action in small characteristic. I will explain an interplay between groups and K3-like varieties such as cubic 4-folds.
Speaker: Shigeru Mukai
Abstract: Only three finite simple groups can act on a K3 surface bi-holomorphically: A_5, A_6 and L_2(7). Bigger ones can act in the following variations:\r\n • K3 surfaces over a field of positive characteristic p > 0,\r\n • holomorphic symplectic manifolds of type K3^[n] and OG10, and\r\n • (= 1+2) symplectic manifolds in positive characteristic.\r\nFor example, the alternating group A_7 act birationally in the case both 1 and 2. The most interesting but still conjectural is the case 3. Sporadic groups Higman-Sims (HS), McLaughlin (McL) and two Conway groups (Co_2 and Co_3) are expected to have a birational action in small characteristic. I will explain an interplay between groups and K3-like varieties such as cubic 4-folds.
Tuesday, November 17th, 2026
Math Event: Geometry/Topology Seminar: Ayush Khaitan - Computing renormalized curvature integrals and conformal invariants of submanifolds
Time: 4:00 PM - 5:15 PM
Location: P-131
Speaker: Ayush Khaitan
Abstract: Abstract: We describe an explicit method for constructing conformal invariants of submanifolds of arbitrary codimension in general conformal manifolds. We apply this method to compute renormalized curvature integrals on Poincaré–Einstein manifolds and their minimal submanifolds, without assuming Alexakis-type decomposition formulas. Time permitting, we will discuss applications to geometric rigidity. This is joint work with Jeffrey Case, Yueh-Ju Lin, Aaron Tyrrell, and Wei Yuan.
Speaker: Ayush Khaitan
Abstract: Abstract: We describe an explicit method for constructing conformal invariants of submanifolds of arbitrary codimension in general conformal manifolds. We apply this method to compute renormalized curvature integrals on Poincaré–Einstein manifolds and their minimal submanifolds, without assuming Alexakis-type decomposition formulas. Time permitting, we will discuss applications to geometric rigidity. This is joint work with Jeffrey Case, Yueh-Ju Lin, Aaron Tyrrell, and Wei Yuan.
Wednesday, November 18th, 2026
Math Event: Algebraic Geometry Seminar: Mingjia Zhang - Intersection cohomology of Shimura varieties
Time: 4:00 PM - 5:00 PM
Location:
Speaker: Mingjia Zhang
Abstract: Let q=e^{2\pi iz}, where z is the coordinate on the complex upper half plane. The discriminant modular form is defined as the infinite product q\prod_n(1-q^n)^24. Ramanujan conjectured that the Fourier coefficients of the power series expansion of this product have explicit bounds. This is proven by Deligne using the intersection cohomology of the modular curve and purity. I will explain Deligne's proof of Ramanujan's conjecture and how it generalizes to higher dimensions. This talk is mostly expository, with certain materials based on joint work with Caraiani-Hamann.
Speaker: Mingjia Zhang
Abstract: Let q=e^{2\pi iz}, where z is the coordinate on the complex upper half plane. The discriminant modular form is defined as the infinite product q\prod_n(1-q^n)^24. Ramanujan conjectured that the Fourier coefficients of the power series expansion of this product have explicit bounds. This is proven by Deligne using the intersection cohomology of the modular curve and purity. I will explain Deligne's proof of Ramanujan's conjecture and how it generalizes to higher dimensions. This talk is mostly expository, with certain materials based on joint work with Caraiani-Hamann.
Thursday, November 19th, 2026
Math Event: Colloquium: Philip Engel - Complex structures on S^6
Time: 2:15 PM - 3:15 PM
Location: Math Tower P-131
Speaker: Philip Engel
Abstract: Abstract: A recent manuscript written by Claude under the direction of Levent Alpoge constructs a 1-parameter family of compact complex threefolds diffeomorphic to S^6. I will describe the geometric ideas behind the construction, outline the proof, and remark on possible future research directions.
Speaker: Philip Engel
Abstract: Abstract: A recent manuscript written by Claude under the direction of Levent Alpoge constructs a 1-parameter family of compact complex threefolds diffeomorphic to S^6. I will describe the geometric ideas behind the construction, outline the proof, and remark on possible future research directions.