For the full schedule of talks please visit: https://scgp.stonybrook.edu/archives/46158

Lecture: 4:00pm, Room 103
Wine and cheese reception: 5:00pm, SCGP Lobby

Title:   Randomness

Abstract:   Is the universe inherently deterministic or probabilistic? Perhaps more importantly - can we tell the difference between the two? Humanity has pondered the meaning and utility of randomness for millennia. There is a remarkable variety of ways in which we utilize perfect coin tosses to our advantage: in statistics, cryptography, game theory, algorithms, gambling... Indeed, randomness seems indispensable!

Which of these applications survive if the universe had no randomness in it at all? Which of them survive if only poor-quality randomness is available, e.g. that arises from "unpredictable" phenomena like the weather or the stock market?

A computational theory of randomness, developed in the past four decades, reveals (perhaps counter-​intuitively) that very little is lost in such deterministic or weakly random worlds. In the talk I'll explain the main ideas and results of this theory.

Erik Paemurru, Bulgarian Academy of Sciences
Local inequalities for cA_k singularities

We generalize an intersection-theoretic local inequality of Fulton–Lazarsfeld to weighted blowups. Using this together with the classification of 3-dimensional divisorial contractions, we prove nonrationality of many families of terminal Fano 3-folds. This is joint work with Igor Krylov and Takuzo Okada

Colin Carr cello
Kyungwha Chu piano

Beethoven Sonata no. 3 in A major
Allegro ma non tanto
Scherzo: Allegro molto
Adagio cantabile - Allegro vivace

Franck Sonata in A major
Allegretto ben moderato
Allegro
Ben moderato: Recitativo-Fantasia
Allegretto poco mosso

For more information please visit: https://scgp.stonybrook.edu/archives/46958

This is a special lecture for local high school students and Stony Brook undergraduate students:

Title:   What is computation?

Abstract:   In this introductory talk, I will explain some of the main ideas underlying the computer revolution, electronic commerce, artificial intelligence and role of computation in understanding nature.

This talk is designed for high-school students, and will leave plenty of time for questions and discussion with the audience.

Title:   The Value of Errors in Proofs
(a fascinating journey from Turing’s 1936 R != RE to the 2020 breakthrough of MIP* = RE )

Abstract:   In the year 2020, a group of theoretical computer scientists posted a paper on the Arxiv with the strange-looking title "MIP* = RE", impacting and surprising not only complexity theory but also some areas of math and physics. Specifically, it resolved several long-standing problems in these areas.

You can find the paper here: https://arxiv.org/abs/2001.04383

As it happens, both acronyms MIP* and RE represent proof systems, of a very different nature. To explain them, we'll take a meandering journey through the classical and modern definitions of proof. I hope to explain how the methodology of computational complexity theory, especially modeling and classification (both problems and proofs) by algorithmic efficiency, naturally leads to the generation of new such notions and results (and more acronyms, like NP). A special focus will be on notions of proof which allow interaction, randomness, and errors, and their surprising power and magical properties.

This talk requires no special mathematical background.

Speaker:   Tom Banks
Title:    Hilbert Bundles, Holographic Space-time and Black Holes

Mohammed Abouzaid, Stanford
100 Years of Morse theory (Note the special time)

Marston Morse developed what became to be known as Morse theory in a papers that appeared in 1925. This lecture will begin by re-casting Morse's results in modern terms, using the formalism that Witten developed in the 1980s, in terms of the existence of a chain complex, built from the critical points of a function and the gradient flow lines connecting them, and whose homology computes ordinary homology. I will then describe modern developments, initiated by Floer, for describing more delicate information about a manifold, using gradient flow trajectories, than are encoded in ordinary homology. Finally, I will address some of the motivations for the recent progress, arising in the areas of symplectic topology and Hamiltonian dynamics.

Stefano Marmi, Scuola Normale Superiore, Pisa
TBA

David Gabai, Princeton University
TBA

Daigo Ito, UC Berkeley
A derived category analogue of the Nakai–Moishezon criterion

In the study of derived categories of coherent sheaves, ample line bundles play a fundamental role: their tensor powers generate the derived category. This raises a natural question: does this generation property characterize ampleness? The answer is negative, but we show that this categorical property can be checked by a classical numerical criterion naturally extending the Nakai–Moishezon criterion. Moreover, the cone of divisors satisfying this condition lies between the big cone and the ample cone. In this talk I will focus on explaining the case of surfaces, where the geometry becomes especially clear

Lu Wang, Yale
TBA

Speaker:   Keith Glennon    

Title:   E11 Symmetries in M Theory    

Abstract:   We review the argument that E11 is a symmetry of m-theory at low energies. We will suggest the possibility of an E11 symmetry based on dimensionally reduced coset symmetries of 11D SUGRA. We will argue that a certain induced representation of the semi-direct product of the very extended algebra E8+++ = E11, with its vector representation, results in the equations of motion of the bosonic sector of m-theory at low energies, predicting additional effects beyond the supergravity approximation. We will then review recent developments illustrating K27 as the 26D closed bosonic string analogue of E11, and future questions.