On some questions about minimal log discrepancies - Mircea Mustata
Mircea Mustata University of Michigan March 3, 2015 The minimal log discrepancy is a measure of singularities of pairs. While akin to the log canonical threshold, it turns out to be much more difficult to study, with many questions still open. I will discuss a question about the boundedne
From playlist Mathematics
Harold Steinacker - Covariant Cosmological Quantum Space-Time
Covariant Cosmological Quantum Space-Time: Higher-spin and Gravity in the IKKT Matrix Model https://indico.math.cnrs.fr/event/4272/attachments/2260/2717/IHESConference_Harold_STEINACKER.pdf
From playlist Space Time Matrices
The weirdest paradox in statistics (and machine learning)
🌏 AD: Get Exclusive NordVPN deal here ➼ https://nordvpn.com/mathemaniac. It's risk-free with Nord's 30-day money-back guarantee! ✌ Second channel video: https://www.youtube.com/watch?v=3ne9yghOtw8 Stein's paradox is of fundamental importance in modern statistics, introducing concepts of
From playlist Novel topics (not in usual math curricula)
Andrew Putman - The Steinberg representation is irreducible
The Steinberg representation is a topologically-defined representation of groups like GL_n(k) that plays a fundamental role in the cohomology of arithmetic groups. The main theorem I will discuss says that for infinite fields k, the Steinberg representation is irreducible. For finite field
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Newton's Identity, Lesson 6.2: Computation of Cubic Discriminant by Vandermonde Matrix
In previous lecture, we use two methods to calculate the expression of discriminant of cubic equations in terms of elementary symmetric polynomials. We now use yet another method to calculate the discriminant: the Vandermonde Matrix
From playlist Newton's Identity for polynomials
Could it be that either quantum mechanics or general relativity is wrong?
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From playlist Science Unplugged: Quantum Mechanics
Albert Einstein, Holograms and Quantum Gravity
In the latest campaign to reconcile Einstein’s theory of gravity with quantum mechanics, many physicists are studying how a higher dimensional space that includes gravity arises like a hologram from a lower dimensional particle theory. Read about the second episode of the new season here:
From playlist In Theory
On the Propogation of Uncertainty in Network Summaries: Eric Kolaczyk, Boston University
http://math.bu.edu/people/kolaczyk/biography.html Eric Kolaczyk was born in 1968 in Chicago, Illiinois. He obtained a BS degree in mathematics from the University of Chicago, and MS and PhD degrees in statistics from Stanford University. He has been on the faculty in the Department of Mat
From playlist Turing Seminars
Ciprian Demeter: Decoupling theorems and their applications
We explain how a certain decoupling theorem from Fourier analysis finds sharp applications in PDEs, incidence geometry and analytic number theory. This is joint work with Jean Bourgain. The lecture was held within the framework of the Hausdorff Trimester Program Harmonic Analysis and Part
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
Algebraic and Complex Geometry | Analysis and Operator Algebras Invited Lecture 4.1 | 8.1 Kähler–Einstein metrics on Fano manifolds: variational and algebro-geometric aspects Sébastien Boucksom Abstract: I will describe a variational approach to the existence of Kähler–Einstein metrics o
From playlist Algebraic & Complex Geometry
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Henry Adams (3/22/22): Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
The Gromov-Hausdorff distance between two metric spaces is an important tool in geometry, but it is difficult to compute. For example, the Gromov-Hausdorff distance between unit spheres of different dimensions is unknown in nearly all cases. I will introduce recent work by Lim, MĂ©moli, and
From playlist Vietoris-Rips Seminar
Adaptive Sampling via Sequential Decision Making - András György
The workshop aims at bringing together researchers working on the theoretical foundations of learning, with an emphasis on methods at the intersection of statistics, probability and optimization. Lecture blurb Sampling algorithms are widely used in machine learning, and their success of
From playlist The Interplay between Statistics and Optimization in Learning
IGA: Quang Tuan Dang - Kähler Einstein metrics on log canonical varieties of general type
Abstract: In this talk, we introduce the notion of (singular) K ähler-Einstein metrics on mildly singular varieties. Extending Di Nezza-Lu’s approach to the setting of big cohomology classes, we show that singlar Kähler-Einstein metrics on log canonical varieties of general type have conti
From playlist Informal Geometric Analysis Seminar
Jeremiah Birrell (U Mass) -- Interpolating Between f-Divergences and Wasserstein Metrics
I will present a general framework for constructing new information-theoretic divergences that interpolate between and combine crucial properties of both Wasserstein metrics and f-divergences. Specifically, these divergences are nontrivial in the presence of heavy tails and when there is a
From playlist Northeastern Probability Seminar 2020
The inability of scientists to create a theory of quantum gravity arises from long-standing tensions between general relativity and quantum mechanics. There have been few approaches with any success. In this video, Fermilab’s Dr. Don Lincoln explains one of the few promising ideas, calle
From playlist Quantum Physics
Wolfram Physics II: Emergent Hypergraph Geometry and General Relativity
Find more information about the summer school here: https://education.wolfram.com/summer/school Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/physics-announcement Find the tools to build a universe: https:
From playlist Wolfram Summer Programs
Inertia: What it is and what it is not?
Describes what inertia is and some common misconceptions about inertia. You can see a listing of all my videos at my website, http://www.stepbystepscience.com
From playlist Mechanics
Jon Lee: Comparing polyhedral relaxations via volume
With W. Morris in 1992, I introduced the idea of comparing polytopes relevant to combinatorial optimization via calculation of n-dimensional volumes. I will review some of that work (related to fixed-charge problems) and describe some new work, with E. Speakman, relevant to the spatial bra
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"