Symplectic geometry | Algebraic geometry
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathematical predictions have since been proven rigorously. Today, mirror symmetry is a major research topic in pure mathematics, and mathematicians are working to develop a mathematical understanding of the relationship based on physicists' intuition. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theory, the formalism that physicists use to describe elementary particles. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow. (Wikipedia).
Mirror symmetry for character varieties and field theory by Sergey Galkin
Date/Time: Wednesday, March 4, 2:00 pm Title: Mirror symmetry for character varieties and field theory Abstract: In a joint work in progress with Swarnava Mukhopadhyay and Pieter Belmans we use mirrors for projective threespaces as building blocks to construct mirrors for moduli spaces o
From playlist Seminar Series
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than
From playlist Physics
Alessandro Chiodo - Towards a global mirror symmetry (Part 1)
Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the i
From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten
Homological Mirror Symmetry - Nicholas Sheridan
Nicholas Sheridan Massachusetts Institute of Technology; Member, School of Mathematics February 11, 2013 Mirror symmetry is a deep conjectural relationship between complex and symplectic geometry. It was first noticed by string theorists. Mathematicians became interested in it when string
From playlist Mathematics
http://www.teachastronomy.com/ A lot of fundamental concepts in physics are based on the idea of symmetry. Symmetry is familiar to us in an aesthetic sense. It often means things that have pleasing proportion, or look the same from every direction, or have a harmonious nature about them.
From playlist 23. The Big Bang, Inflation, and General Cosmology 2
Is string theory a unified theory?
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: String Theory
Lecture 7 | String Theory and M-Theory
(November 1, 2010) Leonard Susskind discusses the specifics of strings including Feynman diagrams and mapping particles. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced our understanding of
From playlist Lecture Collection | String Theory and M-Theory
To learn to think like a scientist check out http://Brilliant.org/SpaceTime PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE Check out the new Space Time Merch Store! https://pbsspacetime.com/ Support Space Time on Patreo
From playlist Understanding the Holographic Universe
Our Antimatter, Mirrored, Time-Reversed Universe
PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE ↓ More info below ↓ Check out the new Space Time Merch Store! https://pbsspacetime.com/ Support Space Time on Patreon https://www.patreon.com/pbsspacetime The foundations o
From playlist Space Time!
Lectures on Homological Mirror Symmetry II - Sheridan Nick
Lectures on Homological Mirror Symmetry Sheridan Nick Institute for Advanced Study; Member, School of Mathematics November 4, 2013
From playlist Mathematics
Knot Categorification From Mirror Symmetry (Lecture- 3) by Mina Aganagic
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)
What is the goal of string theory?
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: String Theory
From the Fukaya category to curve counts via Hodge theory - Nicholas Sheridan
Nicholas Sheridan Veblen Research Instructor, School of Mathematics September 26, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Topological Strings and String Dualities by Rajesh Gopakumar
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Topological Strings and String Dualities (Lecture - 02) by Rajesh Gopakumar
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Calabi-Yau mirror symmetry: from categories to curve-counts - Tim Perutz
Tim Perutz University of Texas at Austin November 15, 2013 I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds. We show (i) that Kontsevich's homological mirror symmetry (HMS) conjecture is a consequence of a fragment of
From playlist Mathematics
Knot Categorification From Mirror Symmetry (Lecture- 2) by Mina Aganagic
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)
In this video I explain why so many physicists believe in string theory but that it also comes with a number of problems. It requires the existence of additional dimensions of space (which we do not see), of new particles (which we do not see), and of new fields (leading to deviations from
From playlist Physics