Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Homotopy type theory: working invariantly in homotopy theory -Guillaume Brunerie
Short talks by postdoctoral members Topic: Homotopy type theory: working invariantly in homotopy theory Speaker: Guillaume Brunerie Affiliation: Member, School of Mathematics Date: September 26, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Lecture 14: The Definition of TC
In this video, we finally give the definition of topological cyclic homology. In fact, we will give two definitions: the first is abstract in terms of a mapping spectrum spectrum in cyclotomic spectra and then we unfold this to a concrete definition on terms of negative topological cyclic
From playlist Topological Cyclic Homology
Computing homology groups | Algebraic Topology | NJ Wildberger
The definition of the homology groups H_n(X) of a space X, say a simplicial complex, is quite abstract: we consider the complex of abelian groups generated by vertices, edges, 2-dim faces etc, then define boundary maps between them, then take the quotient of kernels mod boundaries at each
From playlist Algebraic Topology
Chromatic homotopy theory - Irina Bobkova
Short talks by postdoctoral members Topic: Chromatic homotopy theory Speaker: Irina Bobkova Affiliation: Member, School of Mathematics Date: September 26, 2017
From playlist Mathematics
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
Group Homomorphisms - Abstract Algebra
A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be
From playlist Abstract Algebra
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Gromov-Witten theory and gauge theory (Lecture 1) by Constantin Teleman
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Synthesis Workshop: Asymmetric Synthesis with Allylboronic Acids with Sybrand Jonker (Episode 44)
In this Research Spotlight episode, we're joined by Sybrand Jonker, who takes us through his work on the synthesis and applications of chiral allylboronic acids. Lead reference: J. Am. Chem. Soc. 2020, 142, 21254-21259. Other references (in order of appearance): Review on preparation of
From playlist Special Topics: Organocatalysis
Algebraic Topology - 11.3 - Homotopy Equivalence
We sketch why that the homotopy category is a category.
From playlist Algebraic Topology
Geometric Langlands and 3d Mirror Symmetry (Lecture 1) by Sam Raskin
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Washington Taylor - How Natural is the Standard Model in the String Landscape?
Mike's pioneering work in taking a statistical approach to string vacua has contributed to an ever-improving picture of the landscape of solutions of string theory. In this talk, we explore how such statistical ideas may be relevant in understanding how natural different realizations of th
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
The Tamagawa Number Formula via Chiral Homology - Dennis Gaitsgory
Dennis Gaitsgory Harvard University March 1, 2012 Let X a curve over F_q and G a semi-simple simply-connected group. The initial observation is that the conjecture of Weil's which says that the volume of the adelic quotient of G with respect to the Tamagawa measure equals 1, is equivalent
From playlist Mathematics
Synthesis Workshop: Enantioselective 1,2-Boronate Rearrangements with Dr. Hayden Sharma (Episode 81)
In this Research Spotlight episode, Dr. Hayden Sharma joins us to share his work on enantioselective, catalytic 1,2-boronate rearrangements, which was carried out in the Jacobsen lab at Harvard. Key paper: Science 2021, 374, 752–757. https://doi.org/10.1126/science.abm0386 Other referenc
From playlist Special Topics: Organocatalysis
A mini-course on vertex operator algebras of N= 2 Superconformal... (Lecture 3) by Madalena Lemos
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Florian Frick (5/9/22): Chirality and quantifying embeddability
The combinatorics of triangulations of a space X provide upper bounds for the topology of the space of embeddings of X into d-dimensional Euclidean space. I will explain the previous sentence and as a consequence present generalizations of classical non-embeddability results. For example,
From playlist Bridging Applied and Quantitative Topology 2022
Samuel Raskin: Spectral decomposition of the principal series category
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
Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine
(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des
From playlist Mathematics
Quasi-topological gauged sigma models, the geometric Langlands program, and knots by Meng-Chwan Tan
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory