In particular, topological strings at higher genera and the notion of holomorphic anomaly. Kodairaspencer theory of gravity and exact results for quantum string amplitudes. May, 2014 we consider the vacuum geometry of supersymmetric theories with 4 supercharges, on a flat toroidal geometry. Emergence and correspondence for string theory black holes. Cumrun vafa is an iranianamerican physicist at harvard university and one of the leading string theorists in the world. You may guess that the place is in brazil because the flag next to cumrun resembles the 1sigma and. Pdf categories for the working mathematician download full. O1 curve, unlike the o2 curve, when shrunk leaves no imprint of singularity in the base.
We study fterms describing coupling of the supergravity to n 1 supersymmetric gauge theories which admit large n expansions. Strominger, henry tye, cumrun vafa, and gabriele veneziano. Using ideas from renormalization group theory we show that the study of catastrophes singularities is a powerful tool in the classification of conformal theories. Cumrun vafa is the hollis professor of mathematicks and natural philosophy in the physics department at harvard university, where he does research and teaches theoretical physics since 1985. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. For certain terms in the action, supersymmetry can forbid an infinite number of possible contributions. It looks like we dont have any biography for cumrun vafa yet be the first to contribute. Translate vafa in english online and download now our free translator to use any time at no charge.
Some physicists claim that the popular landscape of universes in string theory may not exist. On the behavior of sequences of solutions to u1 seibergwitten. Cumrun vafa is the hollis professor of mathematicks and natural philosophy in the physics department at harvard university, where he does. Cumrun vafa is an iranianamerican string theorist from harvard university, which he first joined as a harvard junior fellow.
A fock sheaf for givental quantization coates, tom and iritani, hiroshi, kyoto journal of mathematics, 2018. For any issues related to the tasi 2017 webpage, please contact. Georges obied, hirosi ooguri, lev spodyneiko, cumrun vafa. By studying string loop corrections to superpotential of type ii strings compactified on calabiyau threefolds we find a quantum stringy test and a. Kentaro hori, kentaro hori, sheldon katz, albrecht klemm, rahul pandharipande, richard thomas, cumrun vafa, ravi vakil, eric zaslow this thorough and detailed exposition is the result of an intensive monthlong course sponsored by the clay mathematics institute. The microscopic state counting of the extremal reissnernordstrom black hole performed by andrew strominger and cumrun vafa in 1996 has proven to be a central result in string theory. Special polynomial rings, quasi modular forms and duality of topological strings alim, murad, scheidegger. Conceptual analysis of black hole entropy in string theory. University of colorado boulder, department of physics.
Download pdf categories for the working mathematician book full free. Cumrun vafa is the hollis professor of mathematicks and natural philosophy in the physics department at harvard university. Born in iran in 1960, he moved to the us for higher education where he received his b. Cumrun vafa was born in tehran, iran in 1960 and graduated from alborz boys school. According to our current online database, cumrun vafa has 17 students and 36 descendants. Cumrun vafa is the hollis professor of mathematicks and natural philosophy at harvard university. String theory may create far fewer universes than thought. Instructors in the faculty of arts and sciences must hold a teaching appointment at the rank of lecturer or above. If you do not receive our email in the next couple of minutes,please check your spam folder. Cumrun vafa ravi vakil eric zaslow clay mathematics monographs volume 1 american mathematical society clay mathematics institute mirror symmetry cumrun vafa and eric zaslow, editors 1 ams cmi. We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. All freshman seminar instructors must hold an active harvard university teaching appointment. He is the recipient of the 2008 dirac medal and the 2016 breakthrough prize in fundamental physics. I owe special thanks to raphael gunner for, among many other things, his insightful criticisms at an early stage of writing that helped to shape the overall form of the book, and to robert malley for his gentle but persistent encouragement to go beyond thinking about the book and to.
Broadcasting on trees and the ising model evans, william, kenyon, claire, peres, yuval, and schulman, leonard j. Brezis connects partial differential equations and algebraic topology. Herzlich asked if there are other riemannian manifolds with optimal vafawitten bounds, in particular if the fubini. Pdf mirror symmetry, dbranes and counting holomorphic. The focus is on gravitational aspects and we explain in some detail how gravity is described in string theory in terms of the graviton excitation of the string and through background gravitational fields. Mirror symmetry kentaro hori, kentaro hori, sheldon katz. Categories for the working mathematician available for download and read online in other formats. The string landscape, the swampland, and the missing corner. Topological strings and their physical applications. A few days ago, cumrun vafa of harvard was invited to brazil to speak about the mathematical aspects of string theory in an introductory way.
Examples considered include cosmological, cosmic string and blackhole. Theta functions, modular invariance, and strings springerlink. We also compare holography in the context of superstrings with the similar, but much simpler case of topological string theory. Nov 29, 2017 we study compactifications of the 6d e. Weighted bergman kernels on orbifolds ross, julius and thomas.
Geometric engineering of n 1 quantum field theories sciencedirect. Mirror symmetry and closed string tachyon condensation. In theoretical physics, rajesh gopakumar and cumrun vafa introduced in a series of papers new topological invariants, called gopakumarvafa invariants, that represent the number of bps states on a calabiyau 3fold. Files are available under licenses specified on their description page. Semantic scholar profile for cumrun vafa, with 3955 highly influential citations and 372 scientific research papers. Freshman seminar 23p physics, math and puzzles cumrun vafa w 4. Download pdf 275 kb abstract we conjecture a relation between the sln knot homology, recently introduced by khovanov and rozansky, and the spectrum of bps states captured by open topological strings. This file contains additional information such as exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. We obtain an exactly soluble and more or less realistic method of string compactification. Here, with a philosophical readership in mind, the argument is presented in its contemporary context and its rather complex conceptual structure is analysed. The victorian amateur football association is an australian rules football league in victoria, australia.
We study whether such protection can occur in quantum gravity even without sufficient supersymmetry. If you have additional information or corrections regarding this mathematician, please use the update form. We give a brief overview of the string landscape and techniques used to construct string compactifications. Born in iran in 1960, he moved to the usa to study at mit and later princeton university, where he received his ph. Witten was born august 26, 1951 in baltimore, maryland, to a jewish family.
Their combined citations are counted only for the first article. We start by proposing a relation between supersymmetric black holes in four and ve. In this episode of philosophy for our times, cumrun vafa, maryjane rubenstein and john ellis go in search for the meaning of the multiverse. Modular forms and elliptic genera for ale spaces eguchi, tohru, sugawara, yuji, and taormina, anne, 2011. By embedding n2 gauge theories in string theory and utilizing string dualities we map the counting. Some general aspects of string landscape and swamplandwhy do we believe in the existence of ds space. They lead to the following generating function for the gromovwitten invariants on a calabiyau 3fold m. Catastrophes and the classification of conformal theories. Jul 30, 2018 string theory may create far fewer universes than thought. In particular we identify n 1 field theories in four dimensions corresponding to compactifications on arbitrary riemann surfaces with punctures and with arbitrary non.
Vafa nonhyperbolicityofcymanifolds kobayashinonhyperbolicityof calabiyaumanifolds viamirror symmetry ljudmila kamenova1, cumrun vafa2 abstract a compact complex manifold is kobayashi nonhyperbolic if there exists an entire curve on it. Hecke modular form expansions for eighth order mock theta functions srivastava, bhaskar, tokyo journal of mathematics, 2005. Nuclear physics b vol 447, issues 23, pages 195539 7. The conference and this volume are testimonies and celebrations of this unity. The key ingredient in this derivation is the observation that the chiral ring of the. In the case of 3 dimensions, the parameter space is t 2. The unity of mathematics and physics cannot be separated from the life and work of israel gelfand. We show that these fterms are given by summing over genus one nonplanar diagrams of the large n expansion of the associated matrix model or more generally bosonic gauge theory. After covering the relevant background material, the main part of the monograph is devoted to the proof of mirror symmetry from various viewpoints. Both papers focus on andrew strominger and cumrun vafa s groundbreaking 1996 calculation, which analysed the black hole in terms of dbranes. R thomas, s katz, c vafa, r pandharipande, a klemm, r vakil.
String propagation on the quotient of a flat torus by a discrete group is considered. The operator algebra of orbifold models springerlink. Cumrun vafa, mirror symmetry, talk at string theory at the millennium, caltech, january 2000 slides html strings, and the magic of extra dimensions, public talk at icts, bangalore, june 20 pdf. Freshman seminar 23p physics, math and puzzles cumrun. The ones marked may be different from the article in the profile. All structured data from the file and property namespaces is available under the creative commons cc0 license. Dec 27, 2004 project euclid mathematics and statistics online. Topological strings and their physical applications by andrew neitzke, cumrun vafa. Cumrun vafa on stringing the universe together huffpost. We provide evidence for a more natural reformulation of type iib theory in terms of ftheory. Just click the edit page button at the bottom of the page or learn more in the biography submission guide. Here, with a philosophical readership in mind, the argument is presented in its.
To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 18845 for the advisor id. Born in iran in 1960, he moved to the united states in 1977 to receive his b. Swampland and cosmology cumrun vafa harvard university. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. We construct compact examples of dmanifolds for type iib strings. He is well known for his joint work on developing a way to calculate black hole entropy and shedding light on some work of stephen hawking. He came to the us in 1977 and completed his undergraduate degree from massachusetts institute of technology with a major in physics and mathematics.
Freshman seminar 23p physics, math and puzzles cumrun vafa w. He became interested in physics as a young child, specifically how the moon was not falling from the sky, and he later grew his interests in math by high school and was fascinated by how mathematics could predict the movement of objects. Michael bershadsky, sergio cecotti, hirosi ooguri, cumrun vafa. A compact complex manifold is kobayashi nonhyperbolic if there exists an entire curve on it. Cumrun vafa was born in tehran, iran on 1 august 1960. Cumrun vafa using the recent advances in our understanding of nonperturbative aspects of type 11 strings we show how nontrivial exact results for n 2 quantum field theories can be reduced to t. Microscopic origin of the bekensteinhawking entropy. This page was last edited on 25 january 2020, at 04. Knot invariants and topological strings unt digital library. The first paper gives a conceptual analysis of the strominger vafa argument, and of several research efforts that it engendered. Nov 02, 2017 we give a brief overview of the string landscape and techniques used to construct string compactifications. Despite the complexity of the universe the fundamental laws of physics are rather simple, if viewed properly. Pdf emergence and correspondence for string theory black. Cumrun vafa je erson laboratory of physics harvard university cambridge, ma 028 phone.
Mirror symmetry by cumrun vafa, eric zaslow download link. The 2 dimensional vacuum geometry is known to be captured by the tt geometry. Pdf the string landscape and the swampland semantic scholar. Cumrun vafa1 lyman laboratory of physics harvard university cambridge, ma 028, usa aspects of duality and mirror symmetry in string theory are discussed. Some analytic aspects of vafawitten twisted n 4 supersymmetric yangmills theory, ph. Cumrun vafa is an iranianamerican string theorist and educator, and a professor of physics at. He became interested in physics as a young child, specifically how the moon was not falling from the sky, and he later grew his interests in math by high school and was fascinated by how mathematics could predict the movement of.