Thursday, May 9th, 2024
Simons Lectures in Mathematics: Assaf Naor
Time: 11:00 AM - 12:15 PM
Location: 103
Title: Unplanned consequences of the Ribe program, part III: Structure
Speaker: Assaf Naor (Princeton University)
Abstract: Almost 50 years ago, Martin Ribe proved a remarkable geometric rigidity theorem for normed spaces. This inspired an intricate web of conjectures and analogies that aims to transfer phenomena, concepts and intuitions from the structured realm of linear spaces to the seemingly uncontrollably diverse world of general metric spaces. While research on this program has led to powerful, creative and deep discoveries, numerous mysteries remain. These talks will start by introducing the audience to the aforementioned research endeavor, which is known today as the “Ribe program,” assuming no prior knowledge of it. This program naturally enhanced our understanding of the structure of normed spaces, and we will indeed present examples of this, but our main focus will quickly shift to describing some of its unplanned applications. Namely, we will demonstrate how it informs us about objects that are further afield, such as groups, curvature, algorithms and probability.
Title: Unplanned consequences of the Ribe program, part III: Structure
Speaker: Assaf Naor (Princeton University)
Abstract: Almost 50 years ago, Martin Ribe proved a remarkable geometric rigidity theorem for normed spaces. This inspired an intricate web of conjectures and analogies that aims to transfer phenomena, concepts and intuitions from the structured realm of linear spaces to the seemingly uncontrollably diverse world of general metric spaces. While research on this program has led to powerful, creative and deep discoveries, numerous mysteries remain. These talks will start by introducing the audience to the aforementioned research endeavor, which is known today as the “Ribe program,” assuming no prior knowledge of it. This program naturally enhanced our understanding of the structure of normed spaces, and we will indeed present examples of this, but our main focus will quickly shift to describing some of its unplanned applications. Namely, we will demonstrate how it informs us about objects that are further afield, such as groups, curvature, algorithms and probability.
Math Event: Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: Mohamad Rabah - Fukaya Algebra over \Z
Time: 1:00 PM - 2:30 PM
Location: Math 5-127
Title: Fukaya Algebra over \Z
Speaker: Mohamad Rabah [Stony Brook University]
Abstract: In their book, Fukaya-Oh-Ohta-Ono '09, constructed an A_{infty}-algebra structure on the singular cohomology of a Lagrangian submanifold over the Novikov ring with rational coefficients. Using the recent developments in Symplectic topology, namely Bai-Xu '22 realization of Fukaya-Ono '97 proposal on Normally Complex polynomial perturbations and Abouzaid-McLean-Smith '21 construction of Global Kuranishi charts, we show how to adapt such developments in the setting of Lagrangian Floer Theory, which leads us to an integral version of the above result. In this talk we will go over the necessary notions and background needed to state and prove our results, followed by sketch of proofs. View Details
Title: Fukaya Algebra over \Z
Speaker: Mohamad Rabah [Stony Brook University]
Abstract: In their book, Fukaya-Oh-Ohta-Ono '09, constructed an A_{infty}-algebra structure on the singular cohomology of a Lagrangian submanifold over the Novikov ring with rational coefficients. Using the recent developments in Symplectic topology, namely Bai-Xu '22 realization of Fukaya-Ono '97 proposal on Normally Complex polynomial perturbations and Abouzaid-McLean-Smith '21 construction of Global Kuranishi charts, we show how to adapt such developments in the setting of Lagrangian Floer Theory, which leads us to an integral version of the above result. In this talk we will go over the necessary notions and background needed to state and prove our results, followed by sketch of proofs. View Details
Math Event: Colloquium: Marco Mazzucchelli - SYMPLECTIC CAPACITIES, VITERBO ISOPERIMETRIC CONJECTURE, AND CONTACT MANIFOLDS ALL OF WHOSE REEB ORBITS ARE CLOSED
Time: 4:00 PM - 5:00 PM
Location:
Title: SYMPLECTIC CAPACITIES, VITERBO ISOPERIMETRIC CONJECTURE, AND CONTACT MANIFOLDS ALL OF WHOSE REEB ORBITS ARE CLOSED
Speaker: Marco Mazzucchelli [Ecole normale superieure de Lyon]
Abstract: Symplectic capacities are fundamental invariants that govern many rigidity phenomena in symplectic and contact topology. Their introduction in the 1980s by Ekeland and Hofer was motivated by the celebrated Gromov's non-squeezing theorem: a round ball in the symplectic vector space does not symplectically embed into a symplectic cylinder of smaller radius. A conjecture due to Viterbo from the early 2000s asserts that, among the 2n-dimensional convex bodies of volume one, the round balls are the ones with the largest capacity. In this colloquium talk, I will provide an informal and general overview of some developments in symplectic geometry related to the Viterbo conjecture, including its application to convex geometry, and the study of contact manifolds all of whose Reeb orbits are closed. View Details
Title: SYMPLECTIC CAPACITIES, VITERBO ISOPERIMETRIC CONJECTURE, AND CONTACT MANIFOLDS ALL OF WHOSE REEB ORBITS ARE CLOSED
Speaker: Marco Mazzucchelli [Ecole normale superieure de Lyon]
Abstract: Symplectic capacities are fundamental invariants that govern many rigidity phenomena in symplectic and contact topology. Their introduction in the 1980s by Ekeland and Hofer was motivated by the celebrated Gromov's non-squeezing theorem: a round ball in the symplectic vector space does not symplectically embed into a symplectic cylinder of smaller radius. A conjecture due to Viterbo from the early 2000s asserts that, among the 2n-dimensional convex bodies of volume one, the round balls are the ones with the largest capacity. In this colloquium talk, I will provide an informal and general overview of some developments in symplectic geometry related to the Viterbo conjecture, including its application to convex geometry, and the study of contact manifolds all of whose Reeb orbits are closed. View Details