Monday, May 6th, 2024
Program: Rafael I Nepomechie (University of Miami)
Time: 10:30 AM - 11:30 AM
Location: SCGP 313
Title: Bethe state preparation
Speaker: Rafael I Nepomechie (University of Miami)
Abstract: We consider the problem of preparing exact eigenstates of the spin-1/2 Heisenberg quantum spin chain on a quantum computer. We begin by briefly reviewing the basics of coordinate Bethe ansatz and quantum computing. We then describe an efficient construction of Dicke states, and finally its generalization to Bethe states. The algorithm is explicit, deterministic, and does not use ancillary qubits.
Title: Bethe state preparation
Speaker: Rafael I Nepomechie (University of Miami)
Abstract: We consider the problem of preparing exact eigenstates of the spin-1/2 Heisenberg quantum spin chain on a quantum computer. We begin by briefly reviewing the basics of coordinate Bethe ansatz and quantum computing. We then describe an efficient construction of Dicke states, and finally its generalization to Bethe states. The algorithm is explicit, deterministic, and does not use ancillary qubits.
YITP Event: YITP Seminar Speaker: Kaifeng Bu
Time: 2:30 PM - 3:30 PM
Location: YITP Common Room 125
Title: Magic: A New Frontier of Quantum Science
Abstract: Quantum computation is expected to outperform classical computation, yet understanding the origins of this advantage remains a fundamental challenge. In this talk, I will focus on the quantum feature, called magic, which can support the quantum advantage. I will introduce a quantum convolution to test and measure magic. I will also introduce a coarse-graining map, called the “convolution group”, to perform the classification of many-body states. Finally, I will discuss the possible future directions in this framework.Join Zoom Meetinghttps://stonybrook.zoom.us/j/92329150393?pwd=VldPblhmN1h2c0JSN0FsOStsQ2RGQT09Meeting ID: 923 2915 0393Passcode: 208884
Title: Magic: A New Frontier of Quantum Science
Abstract: Quantum computation is expected to outperform classical computation, yet understanding the origins of this advantage remains a fundamental challenge. In this talk, I will focus on the quantum feature, called magic, which can support the quantum advantage. I will introduce a quantum convolution to test and measure magic. I will also introduce a coarse-graining map, called the “convolution group”, to perform the classification of many-body states. Finally, I will discuss the possible future directions in this framework.Join Zoom Meetinghttps://stonybrook.zoom.us/j/92329150393?pwd=VldPblhmN1h2c0JSN0FsOStsQ2RGQT09Meeting ID: 923 2915 0393Passcode: 208884
Tuesday, May 7th, 2024
Simons Lectures in Mathematics: Assaf Naor
Time: 2:15 PM - 3:30 PM
Location: 103
Title: Unplanned consequences of the Ribe program, part I: Introduction
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 I: Introduction
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.
Wednesday, May 8th, 2024
Physics Seminar: Vladimir Rosenhaus
Time: 1:00 PM - 2:00 PM
Location: 313
Title: Wave turbulence and quantum field theory
Abstract: Wind blows over the ocean, exciting long wavelength waves, whose energy then cascades to shorter wavelength waves. The state is statistically stationary and the measured spectrum of energy per mode is a power law, over some range of scales. At very short scales there is sea foam (whitecaps), and the spectrum is believed to again be power law, but a different power. At long scales the nonlinearity is weak (if the wind is not too strong and the waves are small) and the spectrum can be derived analytically. At short scales the nonlinearity is strong, and one loses analytic control. Wave turbulence has been studied theoretically and experimentally in a wide range of systems for half a century. To date, all theoretical results have been at leading order in the nonlinearity. We demonstrate how wave turbulence — a stochastic classical system — can be turned into a quantum field theory. The computation of the spectrum becomes a problem of computing correlation functions. This gives a scheme for computing beyond leading order in the nonlinearity. We consider wave turbulence in a large N system, allowing us to study strong wave turbulence. We develop the analog of the epsilon expansion, allowing us to go from one power law spectrum in the UV to a slightly different power law in the IR (the analog of flow between critical points).
Title: Wave turbulence and quantum field theory
Abstract: Wind blows over the ocean, exciting long wavelength waves, whose energy then cascades to shorter wavelength waves. The state is statistically stationary and the measured spectrum of energy per mode is a power law, over some range of scales. At very short scales there is sea foam (whitecaps), and the spectrum is believed to again be power law, but a different power. At long scales the nonlinearity is weak (if the wind is not too strong and the waves are small) and the spectrum can be derived analytically. At short scales the nonlinearity is strong, and one loses analytic control. Wave turbulence has been studied theoretically and experimentally in a wide range of systems for half a century. To date, all theoretical results have been at leading order in the nonlinearity. We demonstrate how wave turbulence — a stochastic classical system — can be turned into a quantum field theory. The computation of the spectrum becomes a problem of computing correlation functions. This gives a scheme for computing beyond leading order in the nonlinearity. We consider wave turbulence in a large N system, allowing us to study strong wave turbulence. We develop the analog of the epsilon expansion, allowing us to go from one power law spectrum in the UV to a slightly different power law in the IR (the analog of flow between critical points).
Simons Lectures in Mathematics: Assaf Naor
Time: 2:15 PM - 3:30 PM
Location: 103
Title: Unplanned consequences of the Ribe program, part II: Obstructions
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 II: Obstructions
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.
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 $\mathbb{Z}$
Time: 1:00 PM - 2:30 PM
Location: Math 5-127
Title: Fukaya Algebra over $\mathbb{Z}$
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 $\mathbb{Z}$
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
Friday, May 10th, 2024