There are no events at the Simons Center today. Here are the events for this week
Monday, April 21st, 2025
Math Event: Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: Johan Asplund - Persistence of unknottedness of clean Lagrangian intersections
Time: 12:30 PM - 1:55 PM
Location: Math P-131
Title: Persistence of unknottedness of clean Lagrangian intersections
Speaker: Johan Asplund [Stony Brook University]
Abstract: Let L and K be two Lagrangian spheres in a six dimensional compact symplectic manifold that intersect cleanly along a circle. Assuming that the clean intersection is an unknot in both L and K, we will explain how the clean intersection must remain unknotted after any Hamiltonian isotopy of L and K that is supported near their union. This is based on joint work with Yin Li. View Details
Title: Persistence of unknottedness of clean Lagrangian intersections
Speaker: Johan Asplund [Stony Brook University]
Abstract: Let L and K be two Lagrangian spheres in a six dimensional compact symplectic manifold that intersect cleanly along a circle. Assuming that the clean intersection is an unknot in both L and K, we will explain how the clean intersection must remain unknotted after any Hamiltonian isotopy of L and K that is supported near their union. This is based on joint work with Yin Li. View Details
Tuesday, April 22nd, 2025
SCGP Weekly Talk by Yu Deng
Time: 1:15 PM - 2:15 PM
Location: 102
Title: Hilbert's sixth problem: derivation of the Boltzmann and fluid equations (I and II)
Abstract: We present recent works with Zaher Hani and Xiao Ma, in which we derive the Boltzmann equation from the hard sphere dynamics in the Boltzmann-Grad limit, for the full time range in which the (strong) solution to the Boltzmann equation exists. This is done in the Euclidean setting in any dimension d at least 2, and in the periodic setting in dimensions 2 and 3. As a corollary, we also derive the corresponding fluid equations from the the hard sphere dynamics. This resolves Hilbert's Sixth Problem pertaining to the derivation of hydrodynamic equations from colliding particle systems, via the Boltzmann equation as the intermediate step. In the first lecture we review the scope of the problem, the set up and historical backgrounds. In the second lecture we discuss the main ideas involved in the proof, and some of the key steps. The two lectures are independent from each other. They will cover similar contents but with emphasis put on different aspects.
Title: Hilbert's sixth problem: derivation of the Boltzmann and fluid equations (I and II)
Abstract: We present recent works with Zaher Hani and Xiao Ma, in which we derive the Boltzmann equation from the hard sphere dynamics in the Boltzmann-Grad limit, for the full time range in which the (strong) solution to the Boltzmann equation exists. This is done in the Euclidean setting in any dimension d at least 2, and in the periodic setting in dimensions 2 and 3. As a corollary, we also derive the corresponding fluid equations from the the hard sphere dynamics. This resolves Hilbert's Sixth Problem pertaining to the derivation of hydrodynamic equations from colliding particle systems, via the Boltzmann equation as the intermediate step. In the first lecture we review the scope of the problem, the set up and historical backgrounds. In the second lecture we discuss the main ideas involved in the proof, and some of the key steps. The two lectures are independent from each other. They will cover similar contents but with emphasis put on different aspects.
Math Event: Geometry/Topology Seminar: Luca di Cerbo - Curvature, Macroscopic Dimensions, and Symmetric Products of Surfaces
Time: 4:00 PM - 5:15 PM
Location: P-131
Title: Curvature, Macroscopic Dimensions, and Symmetric Products of Surfaces
Speaker: Luca di Cerbo [University of Florida]
Abstract: Abstract: In this talk, I will present a detailed study of the curvature and symplectic asphericity properties of symmetric products of surfaces. I show that these spaces can be used to answer nuanced questions arising in the study of closed Riemannian manifolds with positive scalar curvature. For example, symmetric products of surfaces sharply distinguish between two distinct notions of macroscopic dimension introduced by Gromov and Dranishnikov. As a natural generalization of this circle of ideas, I will also address the Gromov–Lawson and Gromov conjectures in the Kaehler projective setting and draw new connections between the theories of the minimal model, positivity in algebraic geometry, and macroscopic dimensions. View Details
Title: Curvature, Macroscopic Dimensions, and Symmetric Products of Surfaces
Speaker: Luca di Cerbo [University of Florida]
Abstract: Abstract: In this talk, I will present a detailed study of the curvature and symplectic asphericity properties of symmetric products of surfaces. I show that these spaces can be used to answer nuanced questions arising in the study of closed Riemannian manifolds with positive scalar curvature. For example, symmetric products of surfaces sharply distinguish between two distinct notions of macroscopic dimension introduced by Gromov and Dranishnikov. As a natural generalization of this circle of ideas, I will also address the Gromov–Lawson and Gromov conjectures in the Kaehler projective setting and draw new connections between the theories of the minimal model, positivity in algebraic geometry, and macroscopic dimensions. View Details
Wednesday, April 23rd, 2025
Special Talk for High School and Undergraduate Students by Edward Frenkel
Time: 11:00 AM - 12:30 PM
Location: 102
Title: Math is the Source Code of Human Mind
Title: Math is the Source Code of Human Mind
Physics Seminar: Thomas Dumitrescu
Time: 2:00 PM - 3:00 PM
Location: 313
Title: Fun with Superconducting Vortices
Abstract: I will explore the properties of Abrikosov-Nielsen-Olesen vortex strings -- magnetic flux tubes -- in a simple class of Abelian Higgs models, with different choices of potential. The equations governing these vortices become tractable in the limit of large magnetic flux. I will show that the strings exhibit two sharply distinct phases in this limit. I will then discuss the spectrum of small fluctuations around the strings, as well as the low-energy string effective action for the translational zero modes. I will conclude by comparing and contrasting with the properties of confining flux tubes.
Title: Fun with Superconducting Vortices
Abstract: I will explore the properties of Abrikosov-Nielsen-Olesen vortex strings -- magnetic flux tubes -- in a simple class of Abelian Higgs models, with different choices of potential. The equations governing these vortices become tractable in the limit of large magnetic flux. I will show that the strings exhibit two sharply distinct phases in this limit. I will then discuss the spectrum of small fluctuations around the strings, as well as the low-energy string effective action for the translational zero modes. I will conclude by comparing and contrasting with the properties of confining flux tubes.
Analysis Seminar by Yu Deng
Time: 2:15 PM - 3:15 PM
Location: Math P-131
Title: Hilbert's sixth problem: derivation of the Boltzmann and fluid equations (I and II)
Abstract: We present recent works with Zaher Hani and Xiao Ma, in which we derive the Boltzmann equation from the hard sphere dynamics in the Boltzmann-Grad limit, for the full time range in which the (strong) solution to the Boltzmann equation exists. This is done in the Euclidean setting in any dimension d at least 2, and in the periodic setting in dimensions 2 and 3. As a corollary, we also derive the corresponding fluid equations from the the hard sphere dynamics. This resolves Hilbert's Sixth Problem pertaining to the derivation of hydrodynamic equations from colliding particle systems, via the Boltzmann equation as the intermediate step. In the first lecture we review the scope of the problem, the set up and historical backgrounds. In the second lecture we discuss the main ideas involved in the proof, and some of the key steps. The two lectures are independent from each other. They will cover similar contents but with emphasis put on different aspects.
Title: Hilbert's sixth problem: derivation of the Boltzmann and fluid equations (I and II)
Abstract: We present recent works with Zaher Hani and Xiao Ma, in which we derive the Boltzmann equation from the hard sphere dynamics in the Boltzmann-Grad limit, for the full time range in which the (strong) solution to the Boltzmann equation exists. This is done in the Euclidean setting in any dimension d at least 2, and in the periodic setting in dimensions 2 and 3. As a corollary, we also derive the corresponding fluid equations from the the hard sphere dynamics. This resolves Hilbert's Sixth Problem pertaining to the derivation of hydrodynamic equations from colliding particle systems, via the Boltzmann equation as the intermediate step. In the first lecture we review the scope of the problem, the set up and historical backgrounds. In the second lecture we discuss the main ideas involved in the proof, and some of the key steps. The two lectures are independent from each other. They will cover similar contents but with emphasis put on different aspects.
Math Event: Algebraic Geometry Seminar: Nathan Chen - Revisiting minimal degree curves on hypersurfaces
Time: 4:00 PM - 5:00 PM
Location:
Title: Revisiting minimal degree curves on hypersurfaces
Speaker: Nathan Chen [Harvard University]
Abstract: I will discuss a circle of ideas related to results about minimal degree curves on general hypersurfaces. This is joint work with D. Yang. View Details
Title: Revisiting minimal degree curves on hypersurfaces
Speaker: Nathan Chen [Harvard University]
Abstract: I will discuss a circle of ideas related to results about minimal degree curves on general hypersurfaces. This is joint work with D. Yang. View Details
Thursday, April 24th, 2025
YITP Event: YITP/BNL Joint Seminar Speaker: Josh Ruderman (NYU)
Time: 2:00 PM - 2:30 PM
Location: YITP Common Room 6-125
Title: /b> Origins of Nonthermal Dark Matter
Speaker: /b> Professor Josh Ruderman (NYU)
Abstract: What is the cosmological origin of dark matter? Dark matter may be a thermal relic, with sizable interactions and an equilibrium initial condition. Alternatively, dark matter may have feeble interactions and have never reached equilibrium (as for example in “freeze in” models). In this talk I will discuss some recent ideas for how dark matter could have been produced nonthermally. I will introduce classes of models where dark matter is produced by oscillations, or by a period of exponential growth. Zoom: https://stonybrook.zoom.us/j/99130867192?pwd=gXAErW2ySrDwl3p8EE98TkL7m6PWA6.1
Title: /b> Origins of Nonthermal Dark Matter
Speaker: /b> Professor Josh Ruderman (NYU)
Abstract: What is the cosmological origin of dark matter? Dark matter may be a thermal relic, with sizable interactions and an equilibrium initial condition. Alternatively, dark matter may have feeble interactions and have never reached equilibrium (as for example in “freeze in” models). In this talk I will discuss some recent ideas for how dark matter could have been produced nonthermally. I will introduce classes of models where dark matter is produced by oscillations, or by a period of exponential growth. Zoom: https://stonybrook.zoom.us/j/99130867192?pwd=gXAErW2ySrDwl3p8EE98TkL7m6PWA6.1
Math Event: Colloquium: Joshua Greene - Inscription problems and symplectic geometry
Time: 2:15 PM - 3:15 PM
Location:
Title: Inscription problems and symplectic geometry
Speaker: Joshua Greene [Boston College]
Abstract: The square peg problem was posed by Otto Toeplitz in 1911. It asks whether every Jordan curve in the place contains the vertices of a square, and it is still open to this day. I will survey the approaches to this problem and its relatives using symplectic geometry. This talk is based on joint work with Andrew Lobb. View Details
Title: Inscription problems and symplectic geometry
Speaker: Joshua Greene [Boston College]
Abstract: The square peg problem was posed by Otto Toeplitz in 1911. It asks whether every Jordan curve in the place contains the vertices of a square, and it is still open to this day. I will survey the approaches to this problem and its relatives using symplectic geometry. This talk is based on joint work with Andrew Lobb. View Details
Technical Talk for Faculty and Advanced Graduate Students by Edward Frenkel
Time: 4:00 PM - 5:30 PM
Location:
Title: New Frontiers in the Langlands Program for Riemann Surfaces
Abstract: The Langlands correspondence for Riemann surfaces (complex algebraic curves) has two different versions. One (called geometric or categorical), due to Beilinson and Drinfeld, is in terms of sheaves. It has been studied extensively for more than 3 decades, and a version of it was recently proved by a team led by Gaitsgory and Raskin. The other (called analytic) is in terms of functions, and hence it is more down-to-Earth and closer to the original Langlands correspondence for number fields. It has been developed for the last 6 years by Etingof, Kazhdan, and myself. I will start the lecture with a brief introduction to the original formulation of the Langlands correspondence. I will then explain the setup of both the geometric and the analytic versions for Riemann surfaces and connections between them.
Title: New Frontiers in the Langlands Program for Riemann Surfaces
Abstract: The Langlands correspondence for Riemann surfaces (complex algebraic curves) has two different versions. One (called geometric or categorical), due to Beilinson and Drinfeld, is in terms of sheaves. It has been studied extensively for more than 3 decades, and a version of it was recently proved by a team led by Gaitsgory and Raskin. The other (called analytic) is in terms of functions, and hence it is more down-to-Earth and closer to the original Langlands correspondence for number fields. It has been developed for the last 6 years by Etingof, Kazhdan, and myself. I will start the lecture with a brief introduction to the original formulation of the Langlands correspondence. I will then explain the setup of both the geometric and the analytic versions for Riemann surfaces and connections between them.