In mathematics, the eta invariant of a self-adjoint elliptic differential operator on a compact manifold is formally the number of positive eigenvalues minus the number of negative eigenvalues. In practice both numbers are often infinite so are defined using zeta function regularization. It was introduced by Atiyah, Patodi, and Singer who used it to extend the Hirzebruch signature theorem to manifolds with boundary. The name comes from the fact that it is a generalization of the Dirichlet eta function. They also later used the eta invariant of a self-adjoint operator to define the eta invariant of a compact odd-dimensional smooth manifold. Michael Francis Atiyah, H. Donnelly, and I. M. Singerdefined the signature defect of the boundary of a manifold as the eta invariant, and used this to show that Hirzebruch's signature defect of a cusp of a Hilbert modular surface can be expressed in terms of the value at s=0 or 1 of a Shimizu L-function. (Wikipedia).
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
Michael Wibmer: Etale difference algebraic groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Etale Theta - part 3.1 - The Groupy Definition of Xu
Here we give an alternative description of the ZZ/l cover of the punctured elliptic curve X. Twitter: @DupuyTaylor
From playlist Etale Theta
Weil conjectures 7: What is an etale morphism?
This talk explains what etale morphisms are in algebraic geometry. We first review etale morphisms in the usual topology of complex manifolds, where they are just local homeomorphism, and explain why this does not work in algebraic geometry. We give a provisional definition of etale morphi
From playlist Algebraic geometry: extra topics
Ex 2: Limit Definition - Determine Delta for an Arbitrary Epsilon (Quadratic)
This video explains how to determine an expression of delta for an arbitrary epsilon that can be used to prove a limit exists. http://mathispower4u.com
From playlist Limits
Ex 1: Limit Definition - Determine Delta for an Arbitrary Epsilon (Linear)
This video explains how to determine an expression of delta for an arbitrary epsilon that can be used to prove a limit exists. http://mathispower4u.com
From playlist Limits
Implicit Differentiation 1 - Definition and Basic Concepts
Calculus: We give a procedure for finding tangent lines to graph of equations that are not functions. A checklist is given for using implicit differentiation to obtain y'. An example of a tangent line to the unit circle is given.
From playlist Calculus Pt 1: Limits and Derivatives
Epsilon delta definition of limit explained on an example
Epsilon delta definition of limit made easy
From playlist Summer of Math Exposition Youtube Videos
Thermodynamic Formalism for B-free Dynamical Systems - Joana Kulaga-Przymus
Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory Topic: Thermodynamic Formalism for B-free Dynamical Systems Speaker: Joana Kulaga-Przymus Affiliation: Uniwersytet Mikołaja Kopernika Date: March 01, 2023 Abstract: Given $B \subset N$, we consider the corresponding
From playlist Mathematics
A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll Lecture 3
Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
On a local Lyapunov function for the McKean-Vlasov dynamics by Rajesh Sundaresan
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
6. The Scaling Hypothesis Part 1
MIT 8.334 Statistical Mechanics II: Statistical Physics of Fields, Spring 2014 View the complete course: http://ocw.mit.edu/8-334S14 Instructor: Mehran Kardar In this lecture, Prof. Kardar introduces the Scaling Hypothesis, including the Homogeneity Assumption, Divergence of the Correlati
From playlist MIT 8.334 Statistical Mechanics II, Spring 2014
Epsilon delta limit (Example 3): Infinite limit at a point
This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!
From playlist Calculus
Symmetries & Conservation Laws: A (Physics) Love Story
There is a deep connection in physics between symmetries of nature and conservation laws, called Noether's theorem. In this physics lesson I'll show you how it works. Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up The relationship between symmetries and c
From playlist Hamiltonian Mechanics Sequence
Introductory courses on Arthur packets 5
Wee Teck Gan National University of Singapore, Singapore Hiraku Atobe Hokkaido University, Japan
From playlist Introduction courses to Arthur packets
Mesoscopic aspects of classical transport (Lecture 1) by Christian Maes
PROGRAM : FLUCTUATIONS IN NONEQUILIBRIUM SYSTEMS: THEORY AND APPLICATIONS ORGANIZERS : Urna Basu and Anupam Kundu DATE : 09 March 2020 to 19 March 2020 VENUE : Madhava Lecture Hall, ICTS, Bangalore THIS PROGRAM HAS BEEN MODIFIED ONLY FOR LOCAL (BANGALORE) PARTICIPANTS DUE TO COVID-19 RI
From playlist Fluctuations in Nonequilibrium Systems: Theory and Applications
Sheagan John: Secondary higher invariants, and cyclic cohomology for groups of polynomial growth
Talk by Sheagan John in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on December 2, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Scattering Without Space Time (Lecture 2) Nima Arkani Hamed
Nima Arkani-Hamed Institute for Advanced Study, Princeton, USA 26 Sep 2012, 04:00 PM Seminar Hall, ICTS, IISc campus, Bangalore
From playlist Chandrasekhar Lectures
Hugo Duminil-Copin - Introduction to parafermionic observables
In the early eighties, the physicists Belavin, Polyakov and Zamolodchikov postulated the conformal invariance of critical planar statistical models. This prediction enabled physicists to use Conformal Field Theory in order to formulate many conjectures on these models. From a mathematical
From playlist 8ème Séminaire Itzykson : "Les observables parafermioniques et la physique statistique en 2D"
Etale Theta - Part 02 - Properties of the Arithmetic Jacobi Theta Function
In this video we talk about Proposition 1.4 of Etale Theta. This came out of conversations with Emmanuel Lepage. Formal schemes in the Stacks Project: http://stacks.math.columbia.edu/tag/0AIL
From playlist Etale Theta