Member Seminar Speaker: Puskar Mondal (CMSA) Title: On the Breakdown of Einstein's Gravity Abstract: It is important to understand under which conditions, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein's gravity, this is very closely tied to naked singularity formation and Penrose's weak cosmic censorship conjecture. In this talk, […]
Speaker: Joel D. Hamkins (Notre Dame and Oxford) Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an […]
https://youtu.be/M25cbX5do8Y New Technologies in Mathematics Seminar Speaker: Yuanzhi Li, CMU Dept. of Machine Learning and Microsoft Research Title: Physics of Language Models: Knowledge Storage, Extraction, and Manipulation Abstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training, but can they effectively use this knowledge at inference time? In this work, we show several striking […]
Member Seminar Speaker: Daniel Kapec (CMSA) Title: Black Holes as Quantum Systems Abstract: To an outside observer, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance, the leading order semiclassical approximation to the […]
Speaker: Boaz Barak (Harvard) Title: On Provable Copyright Protection for Generative Model Abstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a […]
CMSA Q and A Seminar Speakers: Xi Yin (Harvard Physics) and Peter Kronheimer (Harvard Math) Topics: Xi Yin: What is string field theory? Peter Kronheimer: What is Seiberg-Witten theory?
https://youtu.be/bRHb-MVExJ4 New Technologies in Mathematics Seminar Speaker: Sean Welleck, CMU, Language Technologies Institute Title: Llemma: an open language model for mathematics Abstract: We present Llemma: 7 billion and 34 billion parameter language models for mathematics. The Llemma models are initialized with Code Llama weights, then trained on the Proof-Pile II, a 55 billion token dataset of […]
Member Seminar Speaker: Iacopo Brivio (CMSA) Title: Extension of pluricanonical forms in positive and mixed characteristics Abstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms, i.e. global sections of $(\Omega^{\dim X}_X)^{\otimes m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth […]
Speaker: Manuel Cortés-Izurdiaga (University of Malaga) Title: Homotopy categories of rings: some properties and consequences in module categories Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the […]
Member Seminar Speaker: Zi Yang Kang Title: Deformations of Landau-Ginzburg models and their fibers Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a […]
Speaker: Matthew Foreman (UC Irvine) Title: Impossibility results in classical dynamical systems Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960's, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems. These questions laid the groundwork for enormous amounts of work, but […]
CMSA Q and A Seminar Speakers: Michael Hopkins (Harvard Math) and Minhea Popa (Harvard Math) Topics: Mike Hopkins: What are topological modular forms? Mihnea Popa: What is the abundance conjecture and why should it to be true?