Speaker:   Oleg Lunin
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Ji Hoon Lee
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Emil Martinec
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Samir Mathur
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Don Marolf
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   David Turton
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Michael Temkin, Hebrew University / IAS
New techniques in resolution of singularities

Since Hironaka's famous resolution of singularities in characteristics zero in 1964, it took about 40 years of intensive work of many mathematicians to simplify the method, describe it using conceptual tools and establish its functoriality. However, one point remained quite mysterious: despite different descriptions of the basic resolution algorithm, it was essentially unique. Was it a necessity or a drawback of the fact that all subsequent methods relied on Hironaka's ideas essentially?

The situation changed in the last decade, when a logarithmic, a weighted and a foliated analogues and generalizations were discovered in works of Abramovich-Temkin-Wlodarzcyk, McQuillan, Quek, Abramovich-Temkin-Wlodarzcyk-Belotto and others. At this stage we can already try to figure out general ideas and principles shared by all these methods and the picture is quite surprising -- it seems that each method is quite determined by its basic setting consisting of the class of geometric objects and basic blowings up one works with. In particular, the classical method is probably the only natural resolution (via principalization) method obtained by blowing up smooth centers in the ambient manifold.

In my talk I'll describe the settings and the methods on a very general level. If time permits, I will add some details about the simplest dream (or weighted) method, which has no memory and improves the singularity invariant by each weighted blowing up. Thus, the algorithm becomes simplest possible and the (modest) price one has to pay consists of extending the setting of varieties (or schemes) and blowings up along smooth centers to the setting of orbifolds and blowings up weighted centers.

Speaker:   Yoav Zigdon
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:    Pierre Heidmann
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Apeaker:  Ramesh Narayan
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Mirjam Cvetic
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Roberto Emparan
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Karola Meszaros, Cornell University
Knot polynomials via polytopes

A good way to understand the coefficients of a univariate polynomial with integer coefficients is to lift it to a “nice” multivariate polynomial with 0,1-coefficients. When the terms of the lift correspond to integer points of a magical polytope called a generalized permutahedron, a particularly nice story unfolds. I will illustrate the above by using it to prove a special case of Fox’s trapezoidal conjecture from 1962 that states that the absolute values of the coefficients of the Alexander polynomial of alternating links form a trapezoidal sequence. This talk is based on joint works with Hafner and Vidinas and with K\’alm\’an and Postnikov.

Speaker:   Ramy Brustein
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Kostas Skenderis
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Title:   Discussion
Hashtag: #workshop

Speaker:   Zhiwei Wang
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Speaker:   Daniel Harlow
Title:   TBA
Abstract:   TBA
Hashtag: #workshop

Title:   Discussion 
Hashtag: #workshop

Paco Torres de lizaur, Universidad de Sevilla
TBA

Alex Kapiamba, Harvard University
TBA

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

Paul Freehan, Rutgers University
TBA

Public holiday

Hanbing Fang, Stony Brook University
Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow

The uniqueness of tangent flows is central to understanding singularity formation in geometric flows. A foundational result of Colding and Minicozzi establishes this uniqueness at cylindrical singularities under the Type I assumption in the Ricci flow. In this talk, I will present a strong uniqueness result for cylindrical tangent flows at the first singular time. Our proof hinges on a Łojasiewicz inequality for the pointed W

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.

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.