Students can begin to submit major/minor changes effective Spring Semester.
Speaker: Egor Shelukhin
Abstract:
I will report on joint work with Shaoyun Bai, Nicholas Wilkins, and Guangbo Xu, obtaining a number of definitive results in Hamiltonian dynamics on arbitrary symplectic manifolds. We rely on characteristic p methods in Floer theory including quantum deformations of Steenrod powers, first suggested by Fukaya, as well as Smith theory in Floer cohomology via the equivariant pants product introduced by Seidel. In particular, we show that, in complete generality, the existence of a symplectically degenerate maximum for a Hamiltonian diffeomorphism implies the existence of infinitely many simple periodic points, resolving an open question arising from the work of Ginzburg and Gürel.
Speaker: Mingyang Li
Abstract:
I will discuss a moduli-space approach to the existence and classification of compact Einstein four-manifolds with torus symmetry. We define virtual counts of smooth toric Einstein metrics on different manifolds and relate them through moduli spaces of conical Einstein metrics. Combining gluing, compactness, and boundary counting leads to a complete diffeomorphism classification: a closed simply connected smooth toric four-manifold supports a toric Einstein metric precisely when \chi>=3|\tau|. This is joint work with Song Sun.
Wednesday, October 28:
Thursday, October 29:
Friday, October 30:
Speaker: Andrew Blumberg
How does AI change mathematical and physical research? This SCGP event connects five research talks with a structured panel. The talks focus on specific research problems. The panel examines proof, understanding, discovery and education. Speakers will compare concrete examples and explain how they check results. Audience questions will connect the three themes.
For the full schedule, please visit: https://scgp.stonybrook.edu/archives/49084Speaker: Myrto Mavraki
Abstract:
I will discuss uniform bounds for algebraic relations between rational maps and for their preperiodic points. For the diagonal in $\mathbb P^1\times\mathbb P^1$, these give uniform bounds on the iterates needed to have a common iterate for non-exceptional maps, and on common preperiodic points unless the preperiodic sets coincide. Both follow from a stability theorem: we show that in maximally varying families of curves, stability is equivalent to a persistent dynamical relation, and, apart from an elliptic exception, any nonzero bifurcation current has nonzero top wedge power. This is joint work with Laura DeMarco.
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Begins for Winter & Spring according to enrollment appointments.
Speaker: Mohan Swaminathan
Abstract:
TBA
Observance
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