Podcasts about chern simons

Michael Freedman is a mathematician who was awarded the Fields Medal in 1986 for his solution of the 4-dimensional Poincare conjecture. Mike has also received numerous other awards for his scientific contributions including a MacArthur Fellowship and the National Medal of Science. In 1997, Mike joined Microsoft Research and in 2005 became the director of Station Q, Microsoft's quantum computing research lab. As of 2023, Mike is a Senior Research Scientist at the Center for Mathematics and Scientific Applications at Harvard University. Patreon (bonus materials + video chat): https://www.patreon.com/timothynguyen In this wide-ranging conversation, we give a panoramic view of Mike's extensive body of work over the span of his career. It is divided into three parts: early, middle, and present day, which respectively include his work on the 4-dimensional Poincare conjecture, his transition to topological physics, and finally his recent work in applying ideas from mathematics and philosophy to social economics. Our conversation is a blend of both the nitty-gritty details and the anecdotal story-telling that can only be obtained from a living legend. I. Introduction 00:00 : Preview 01:34 : Fields Medalist working in industry 03:24 : Academia vs industry 04:59 : Mathematics and art 06:33 : Technical overview II. Early Mike: The Poincare Conjecture (PC) 08:14 : Introduction, statement, and history 14:30 : Three categories for PC (topological, smooth, PL) 17:09 : Smale and PC for d at least 5 17:59 : Homotopy equivalence vs homeomorphism 22:08 : Joke 23:24 : Morse flow 33:21 : Whitney Disk 41:47 : Casson handles 50:24 : Manifold factors and the Whitehead continuum 1:00:39 : Donaldson's results in the smooth category 1:04:54 : (Not) writing up full details of the proof then and now 1:08:56 : Why Perelman succeeded II. Mid Mike: Topological Quantum Field Theory (TQFT) and Quantum Computing (QC) 1:10:54: Introduction 1:11:42: Cliff Taubes, Raoul Bott, Ed Witten 1:12:40 : Computational complexity, Church-Turing, and Mike's motivations 1:24:01 : Why Mike left academia, Microsoft's offer, and Station Q 1:29:23 : Topological quantum field theory (according to Atiyah) 1:34:29 : Anyons and a theorem on Chern-Simons theories 1:38:57 : Relation to QC 1:46:08 : Universal TQFT 1:55:57 : Witten: Donalson theory cannot be a unitary TQFT 2:01:22 : Unitarity is possible in dimension 3 2:05:12 : Relations to a theory of everything? 2:07:21 : Where topological QC is now III. Present Mike: Social Economics 2:11:08 : Introduction 2:14:02 : Lionel Penrose and voting schemes 2:21:01 : Radical markets (pun intended) 2:25:45 : Quadratic finance/funding 2:30:51 : Kant's categorical imperative and a paper of Vitalik Buterin, Zoe Hitzig, Glen Weyl 2:36:54 : Gauge equivariance 2:38:32 : Bertrand Russell: philosophers and differential equations IV: Outro 2:46:20 : Final thoughts on math, science, philosophy 2:51:22 : Career advice   Some Further Reading: Mike's Harvard lecture on PC4: https://www.youtube.com/watch?v=TSF0i6BO1Ig Behrens et al. The Disc Embedding Theorem. M. Freedman. Spinoza, Leibniz, Kant, and Weyl. arxiv:2206.14711   Twitter: @iamtimnguyen   Webpage: http://www.timothynguyen.org

This podcast marks the passing of James Harris Simons, better-known as Jim.The interviewees are John Ewing, David Eisenbud and Andrew Millis.The Simons Foundation - https://www.simonsfoundation.orgSimons Foundation article about Jim's life - https://www.simonsfoundation.org/2024/05/10/remembering-the-life-and-careers-of-jim-simons/Brady's interview with Jim for Numberphile (full hour-log version) - https://www.youtube.com/watch?v=QNznD9hMEh0Shorter 18-minute version - https://www.youtube.com/watch?v=gjVDqfUhXOYMath For America - https://www.mathforamerica.orgThe Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI) - https://www.slmath.orgThe Flatiron Institute - https://www.simonsfoundation.org/flatiron/The Chern-Simons form - https://en.wikipedia.org/wiki/Chern%E2%80%93Simons_formThe Archimedes (Jim's yacht) - https://www.feadship.nl/fleet/archimedes1Numberphile has been supported by The Simons Foundation (via SLMath) for many years. We are yet another of Jim's legacies.You can support Numberphile on Patreon - https://www.patreon.com/numberphileHere are our Patrons - https://www.numberphile.com/patronsNumberphile Podcast by Brady Haran

YouTube link https://youtu.be/9z3JYb_g2QsProf. Peter Woit discusses string theory, its decline, and introduces his graviweak unification theory using Euclidean twistor in Euclidean spacetime. TIMESTAMPS:- 00:00:00 Introduction- 00:00:00 String theory's fundamental issues | Mathematicians' challenges- 00:02:20 Spacetime and twistor theory insights- 00:20:00 Bundles & diffeomorphism groups- 00:38:34 Spinors as a spacetime point- 00:46:57 Dominance of string theory & Ed Witten's influence- 00:54:17 Quest for quantum gravity- 01:03:22 String theory's lack of predictive power  - 01:09:33 Machine learning meets theoretical physics- 01:18:56 Personal attacks vs. intellectual debate- 01:24:49 Mathematicians vs. Physicists | Academic silos- 01:37:15 Developing a contrarian view & the origin of 'Not Even Wrong'- 01:40:54 Langlands & representation theory- 01:48:51 Spacetime is NOT doomed- 01:58:47 Sean Carroll's crisis in physics (odd responses to criticism)- 02:13:21 Differentiable structures by dimension- 02:26:10 Gravi-weak unification & chirality- 02:32:57 Chern-Simons theory- 02:42:20 Gravity as torsion or curvature- 02:50:07 Category theory in physics- 02:56:43 Defining a fulfilling life - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!)- Crypto: https://tinyurl.com/cryptoTOE- PayPal: https://tinyurl.com/paypalTOE- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs- iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802- Pandora: https://pdora.co/33b9lfP- Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e- Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything- TOE Merch: https://tinyurl.com/TOEmerch LINKS MENTIONED:- Not Even Wrong (Peter Woit's Blog): https://www.math.columbia.edu/~woit/wordpress- Not Even Wrong (Peter Woit's Book): https://amzn.to/40NFeaK- Spacetime is Right-Handed (Peter Woit's Article): https://www.math.columbia.edu/~woit/righthanded.pdf | https://www.math.columbia.edu/~woit/wordpress- Podcast w/ Edward Frankel: https://youtu.be/n_oPMcvHbAc- The Elegant Universe (Brian Greene): https://amzn.to/3sNmk7x- The Trouble With Physics (Lee Smolin): https://amzn.to/47lCCUj- Podcast w/ Sabina Hossenfelder on TOE: https://youtu.be/walaNM7KiYA- Podcast w/ Stephon Alexander Part 1: https://youtu.be/VETxb96a3qk  - Podcast w/ Stephon Alexander Λ Sal Pais: https://youtu.be/PE4C7OI7Frg- Podcast w/ Eric Weinstein: https://youtu.be/KElq_MLO1kw- Podcast w/ Stephen Wolfram Part 1: https://youtu.be/1sXrRc3Bhrs- Podcast w/ Stephen Wolfram Part 2: https://youtu.be/xHPQ_oSsJgg- Podcast w/ Jonathan Oppenheim: https://youtu.be/NKOd8imBa2s

YouTube Link: https://www.youtube.com/watch?v=9z3JYb_g2Qs Prof. Peter Woit discusses string theory, its decline, and introduces his graviweak unification theory using Euclidean twistor in Euclidean spacetime. TIMESTAMPS: - 00:00:00 Introduction - 00:00:00 String theory's fundamental issues | Mathematicians' challenges - 00:02:20 Spacetime and twistor theory insights - 00:20:00 Bundles & diffeomorphism groups - 00:38:34 Spinors as a spacetime point - 00:46:57 Dominance of string theory & Ed Witten's influence - 00:54:17 Quest for quantum gravity - 01:03:22 String theory's lack of predictive power - 01:09:33 Machine learning meets theoretical physics - 01:18:56 Personal attacks vs. intellectual debate - 01:24:49 Mathematicians vs. Physicists | Academic silos - 01:37:15 Developing a contrarian view & the origin of 'Not Even Wrong' - 01:40:54 Langlands & representation theory - 01:48:51 Spacetime is NOT doomed - 01:58:47 Sean Carroll's crisis in physics (odd responses to criticism) - 02:13:21 Differentiable structures by dimension - 02:26:10 Gravi-weak unification & chirality - 02:32:57 Chern-Simons theory - 02:42:20 Gravity as torsion or curvature - 02:50:07 Category theory in physics - 02:56:43 Defining a fulfilling life - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Crypto: https://tinyurl.com/cryptoTOE - PayPal: https://tinyurl.com/paypalTOE - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast... - Pandora: https://pdora.co/33b9lfP - Spotify: https://open.spotify.com/show/4gL14b9... - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeveryt... - TOE Merch: https://tinyurl.com/TOEmerch LINKS MENTIONED: - Not Even Wrong (Peter Woit's Blog): https://www.math.columbia.edu/~woit/w... - Not Even Wrong (Peter Woit's Book): https://amzn.to/40NFeaK - Spacetime is Right-Handed (Peter Woit's Article): https://www.math.columbia.edu/~woit/r... - Podcast w/ Edward Frankel: https://youtu.be/n_oPMcvHbAc - The Elegant Universe (Brian Greene): https://amzn.to/3sNmk7x - The Trouble With Physics (Lee Smolin): https://amzn.to/47lCCUj - Podcast w/ Sabina Hossenfelder on TOE: https://youtu.be/walaNM7KiYA - Podcast w/ Stephon Alexander Part 1: https://youtu.be/VETxb96a3qk - Podcast w/ Stephon Alexander Λ Sal Pais: https://youtu.be/PE4C7OI7Frg - Podcast w/ Eric Weinstein: https://youtu.be/KElq_MLO1kw - Podcast w/ Stephen Wolfram Part 1: https://youtu.be/1sXrRc3Bhrs - Podcast w/ Stephen Wolfram Part 2: https://youtu.be/xHPQ_oSsJgg - Podcast w/ Jonathan Oppenheim: https://youtu.be/NKOd8imBa2s

Isotropic cosmic birefringence from early dark energy by Kai Murai et al. on Sunday 18 September A tantalizing hint of isotropic cosmic birefringence has been found in the $E B$ cross-power spectrum of the cosmic microwave background (CMB) polarization data with a statistical significance of $3sigma$. A pseudoscalar field coupled to the CMB photons via the Chern-Simons term can explain this observation. The same field may also be responsible for early dark energy (EDE), which alleviates the so-called Hubble tension. Since the EDE field evolves significantly during the recombination epoch, the conventional formula that relates $E B$ to the difference between the $E$- and $B$-mode auto-power spectra is no longer valid. Solving the Boltzmann equation for polarized photons and the dynamics of the EDE field consistently, we find that currently favored parameter space of the EDE model yields a variety of shapes of the $EB$ spectrum, which can be tested by CMB experiments. arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2209.07804v1

Graham Farmelo is an award-winning biographer and science writer. Based in London, he is a Fellow at Churchill College, Cambridge and a regular visitor at the Institute for Advanced Study, Princeton. He was a lecturer in physics at the Open University, 1977-1990. Briefly the youngest tenured academic in the UK. Quickly specialized as a teacher, chaired the team that produced the Science Foundation Course in the late 1980s and conceived its inter-disciplinary science course ‘Science Matters'. Farmelo is author of 'The Universe Speaks in Numbers', published in May 2019. It explores the relationship between mathematics and the search for the laws of physics, and highlights the contributions of several theoretical physicists, natural philosophers and mathematicians, notably Isaac Newton, Pierre-Simon Laplace, James Clerk Maxwell, Albert Einstein and Paul Dirac. Farmelo's Dirac biography ‘The Strangest Man' won the 2009 Costa Prize for Biography[1] and the 2009 'Los Angeles Times Science and Technology Book Prize'.[2] The book was chosen by Physics World as the physics book of the year in 2009,[3] when it was selected as one of Nature's books of the year. Farmelo's 2013 book 'Churchill's Bomb' focuses on Winston Churchill's role in British nuclear research 1939-53, with hitherto unpublished information on its influence by Churchill's science adviser Frederick Lindemann. The book emphasizes conflicts between scientific opportunity and political direction. Farmelo is critical of Churchill's wavering attention and changes of policy as he aged. https://grahamfarmelo.com/ 00:00:00 Intro 00:02:12 Do we need a theory of everything? 00:04:33 Fundamental Physics is a small part of the whole field. 00:06:55 What is the mathematical language of the Universe? Intergers? Rationale numbers? Other? 00:10:10 We're at an odd time in physics! The standard model works better than expected! 00:16:21 Never say never! What is untestable today may be testable tomorrow. 00:17:04 Bridging Maxwell, Yang-Mills and Chern-Simons and the view of Ed Witten 00:24:19 Is there a role for "beauty" in physics and math? 00:26:50 What rubric could be used to grade candidates for theories of everything? 00:32:22 How to break the standard model. 00:38:41 Is string theory already falsified? What can it tell us now? 00:47:57 How do you engage young people to get inspired in physics today? Where should our resources go? 00:52:51 What mysteries are you currently most engaged with? What did Freeman Dyson mean to you? 00:58:14 Discussing Nima Arkani-Hamed. 01:04:00 What do you think about the work of Gerard 't Hooft?  http://briankeating.com/mailing_list.php 

Daniel Jafferis is a tenured Professor of Physics at Harvard University where he studies String Theory. Daniel matriculated at Yale University at the age of 14, and begun his PhD at age 18, finishing when he was 23-years old. Jafferis's research has focused on string theory and supersymmetric quantum field theory. He is one of the discoverers of the low energy three dimensional superconformal Chern-Simons-matter theory. --- Support this podcast: https://podcasters.spotify.com/pod/show/jake-newfield/support

Quantum mechanical potentials with multiple classically degenerate minima lead to spectra that are determined by the pertaining tunneling amplitudes. For the strong interactions, these classical minima correspond to configurations of a given Chern-Simons number. The tunneling amplitudes are then given by instanton transitions, and the associated gauge invariant eigenstates are the theta-vacua. Under charge-parity (CP) reversal theta changes its sign, and so it is believed that CP-violating observables such as the electric dipole moment of the neutron or the decay of the eta-prime meson into two pions are proportional to theta. Here we argue that this is not the case. This conclusion is based on the assumption that the path integral is dominated by saddle points of finite action and fluctuations around these. In spacetimes of infinite volume, this leads to the requirement of vanishing physical fields at the boundaries. For the gauge fields, this implies topological quantization corresponding to homotopy classes for all integers. We consequently calculate quark correlations by first taking the spacetime volume to infinity and then summing over the sectors. This leads to an absence of CP violation in the quark correlations, in contrast to the conventional way of taking the limits the other way around. While there is an infinite number of homotopy classes in the strong interactions, there is only a finite number of classical vacua for quantum mechanical systems. For the latter the order of taking time to infinity and summing over the transitions is therefore immaterial.

Gauge/Gravity Duality 2013

When Dr. Stephon Alexander listens to the music of the cosmos, he hears structure, but also flexibility. He hears familiar cadences and novel riffs. He hears strings vibrating in ten-dimensional spacetime and resonating loops of quantum gravity. He hears Einstein’s musical mind and Coltrane’s cosmic sensibility. He hears the jazz of physics. And so will you. In this episode, Stephon tells Jocelyn and Bradley how a journey wending through the dusty halls of old jazz clubs and the chalky floors of physics offices ultimately led him from Trinidad to the Bronx to Brown University. He shares how his experience as a jazz saxophonist has shaped his approach to physics, and how incorporating more elements from the improvisational, inclusive culture of jazz will benefit the future of physics. Along the way, he explains how he is working to integrate general relativity with quantum mechanics by uncovering the quantum nature of gravity, and the friends speculate that the answer may ultimately shed light on the origins of consciousness itself. Follow Stephon on Twitter @stephstem, and learn more about his amazing work at the links below! Secret Lives of Scientists on NOVA: https://www.pbs.org/wgbh/nova/video/stephon-alexander-theoretical-physicist/ Big Think:“Sources of Inspiration”: https://bigthink.com/videos/sources-of-inspiration “Beyond Einstein”: https://bigthink.com/videos/beyond-einstein The Jazz of Physics: https://www.amazon.com/Jazz-Physics-Between-Structure-Universe/dp/0465034993 https://www.npr.org/sections/codeswitch/2016/06/11/481664722/scientist-stephon-alexander-infinite-possibilities-unite-jazz-and-physics TEDx Talk San Diego: https://youtu.be/v9_ZzY99-6U “Black Academics Have a Responsibility to the Next Generation” (New York Times editorial) : https://www.nytimes.com/roomfordebate/2013/02/04/do-black-intellectuals-need-to-talk-about-race/black-academics-have-a-responsibility-to-the-next-generation Brown University: https://vivo.brown.edu/display/salexan4 https://www.stephonalexanderlab.com/ Check out some of Stephon’s technical papers: Brane Gases: https://journals.aps.org/prd/pdf/10.1103/PhysRevD.62.103509 Noncommutative inflation: https://journals.aps.org/prd/pdf/10.1103/PhysRevD.67.081301 Gravitational waves: https://journals.aps.org/prd/pdf/10.1103/PhysRevD.67.081301 Chern–Simons modified general relativity: https://www.sciencedirect.com/science/article/pii/S037015730900177X Super strings and baryon asymmetry: https://iopscience.iop.org/article/10.1088/1475-7516/2006/06/018/meta Horava-Lifshitz theory: https://arxiv.org/pdf/1206.6296.pdf A Wrinkle in Time (2018) film trailer: https://youtu.be/UhZ56rcWwRQ John Coltrane music: Giant steps: https://www.youtube.com/watch?v=xy_fxxj1mMY Cosmic music: https://www.youtube.com/watch?v=sC4tmbWzevg Related episodes: Quantum Whaaaat? (Part 1): https://podcasts.apple.com/us/podcast/30-discussion-quantum-whaaaat-part-1/id1471423633?i=1000464036509 Quantum Whatnot (Part 2): https://podcasts.apple.com/us/podcast/31-discussion-quantum-whatnot-part-2/id1471423633?i=1000464036508 The Musical Shape of Science (Tim Blais): https://podcasts.apple.com/us/podcast/61-tim-blais-the-musical-shape-of-science/id1471423633?i=1000492250770

Mathematician, codebreaker, Professor, hedge fund pioneer, & philanthropist Jim Simons makes his first-ever podcast appearance on this episode of INTO THE IMPOSSIBLE with UC San Diego Professor Brian Keating. Learn about Chern-Simons theory, leadership lessons, hedge funds, and a dedication to serve the world through basic research from a master. It is truly a delight to share with you the more personal side of the man who’s been called The World’s Smartest Billionaire: https://youtu.be/gjVDqfUhXOY In this interview, we discuss heroes, fatherhood, leadership and the art of math.    00:15:15 Why he’d invite Abraham Lincoln to dinner. 00:23:42 Discovering Zeno’s paradox at the age of three. 00:34:28 Can math be beautiful? 00:46:25 Lessons from a master investor: alpha vs. beta. 00:56:06 The serendipitous Chern-Simons partnership. 01:03:18 A father’s love. 01:11:09 The legacy of a good example. Jim Simons earned a Ph.D. in mathematics from UC Berkeley at the age of 23. He worked as a mathematician for the NSA and as a professor and department chair at Stony Brook University. Simons earned billions after founding the hedge fund firm Renaissance Technologies. He co-founded the Simons Foundation with his wife Marilyn in 1994 to advance scientific research. The foundation provided funding for the Simons Observatory, a telescope array being built in the Atacama Desert of Northern Chile https://simonsobservatory.org/ Simons also founded Math For America in 2004 to facilitate better math education. Watch a TED interview with Jim Simons https://youtu.be/U5kIdtMJGc8 Learn about the Simons Observatory, including the Simons-National Society of Black Physicists Scholars Program (SNSP) https://simonsobservatory.org/snsp.php Learn more about the Simons Foundation on the web: https://www.simonsfoundation.org follow them on Twitter: https://twitter.com/SimonsFdn Please subscribe, rate, and review the INTO THE IMPOSSIBLE Podcast on iTunes: https://itunes.apple.com/us/podcast/into-the-impossible/id1169885840?mt=2 Learn more about your ad choices. Visit megaphone.fm/adchoices

Strings 2012

In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

In this thesis we study the low-energy effective dynamics emerging from a class of F-theory compactifications in four and six dimensions. We also investigate six-dimensional supersymmetric quantum field theories with self-dual tensors, motivated by the problem of describing the long-wavelength regime of a stack of M5-branes in M-theory. These setups share interesting common features. They both constitute examples of intrinsically non-perturbative physics. On the one hand, in the context of F-theory the non-perturbative character is encoded in the geometric formulation of this class of string vacua, which allows the complexified string coupling to vary in space. On the other hand, the dynamics of a stack of multiple M5-branes flows in the infrared to a novel kind of superconformal field theories in six dimensions - commonly referred to as (2,0) theories - that are expected to possess no perturbative weakly coupled regime and have resisted a complete understanding so far. In particular, no Lagrangian description is known for these models. The strategy we employ to address these two problems is also analogous. A recurring Leitmotif of our work is a transdimensional treatment of the system under examination: in order to extract information about dynamics in $d$ dimensions we consider a (d-1)-dimensional setup. As far as F-theory compactifications are concerned, this is a consequence of the duality between M-theory and F-theory, which constitutes our main tool in the derivation of the effective action of F-theory compactifications. We apply it to six-dimensional F-theory vacua, obtained by taking the internal space to be an elliptically fibered Calabi-Yau threefold, but we also employ it to explore a novel kind of F-theory constructions in four dimensions based on manifolds with Spin(7) holonomy. With reference to six-dimensional (2,0) theories, the transdimensional character of our approach relies in the idea of studying these theories in five dimensions. Indeed, we propose a Lagrangian that is formulated in five dimensions but has the potential to capture the six-dimensional interactions of (2,0) theories. This investigation leads us to explore in closer detail the relation between physics in five and in six dimensions. One of the outcomes of our exploration is a general result for one-loop corrections to Chern-Simons couplings in five dimensions.

Wadia, S (Tata Institute of Fundamental Research) Monday 14 May 2012, 14:00-15:00

Prakash, S (Tata Institute of Fundamental Research) Tuesday 20 March 2012, 14:00-15:00

Yokoyama, S (Tata Institute of Fundamental Research) Tuesday 31 January 2012, 14:00-15:00

Smith, D (University of Durham) Wednesday 01 February 2012, 16:00-17:00

Dimofte, T (Princeton) Thursday 14 April 2011, 10:00-11:00

The Hodge theory arising in homological mirror symmetry. Pure nc Hodge structures and their Betti and de Rham aspects. Categorical nc geometry, variations of nc Hodge structures, nc Deligne cohomology, Griffiths groups, and normal functions. Examples from singularity theory, symplectic topology, and complex geometry. Fukaya and matrix factorization categories. Chern-Simons functionals. Motivic local systems and nc Hodge structures: the Fano case. Mirror maps for del Pezzo surfaces.

The Hodge theory arising in homological mirror symmetry. Pure nc Hodge structures and their Betti and de Rham aspects. Categorical nc geometry, variations of nc Hodge structures, nc Deligne cohomology, Griffiths groups, and normal functions. Examples from singularity theory, symplectic topology, and complex geometry. Fukaya and matrix factorization categories. Chern-Simons functionals. Motivic local systems and nc Hodge structures: the Fano case. Mirror maps for del Pezzo surfaces.

The Hodge theory arising in homological mirror symmetry. Pure nc Hodge structures and their Betti and de Rham aspects. Categorical nc geometry, variations of nc Hodge structures, nc Deligne cohomology, Griffiths groups, and normal functions. Examples from singularity theory, symplectic topology, and complex geometry. Fukaya and matrix factorization categories. Chern-Simons functionals. Motivic local systems and nc Hodge structures: the Fano case. Mirror maps for del Pezzo surfaces.

The Hodge theory arising in homological mirror symmetry. Pure nc Hodge structures and their Betti and de Rham aspects. Categorical nc geometry, variations of nc Hodge structures, nc Deligne cohomology, Griffiths groups, and normal functions. Examples from singularity theory, symplectic topology, and complex geometry. Fukaya and matrix factorization categories. Chern-Simons functionals. Motivic local systems and nc Hodge structures: the Fano case. Mirror maps for del Pezzo surfaces.

The Hodge theory arising in homological mirror symmetry. Pure nc Hodge structures and their Betti and de Rham aspects. Categorical nc geometry, variations of nc Hodge structures, nc Deligne cohomology, Griffiths groups, and normal functions. Examples from singularity theory, symplectic topology, and complex geometry. Fukaya and matrix factorization categories. Chern-Simons functionals. Motivic local systems and nc Hodge structures: the Fano case. Mirror maps for del Pezzo surfaces.

The Hodge theory arising in homological mirror symmetry. Pure nc Hodge structures and their Betti and de Rham aspects. Categorical nc geometry, variations of nc Hodge structures, nc Deligne cohomology, Griffiths groups, and normal functions. Examples from singularity theory, symplectic topology, and complex geometry. Fukaya and matrix factorization categories. Chern-Simons functionals. Motivic local systems and nc Hodge structures: the Fano case. Mirror maps for del Pezzo surfaces.

Jorge Zanelli gives string theory description of the three dimensional black holes.

In dieser Dissertation untersuchen wir die Rolle verallgemeinerter Chern-Simons Terme in vierdimensionalen chiralen Eichtheorien, genauer, wie Quantenanomalien weggehoben werden können. Unter Einbeziehung von verallgemeinerten Chern-Simons Termen und zusätzlichen axionischen Kopplungen ist man in der Lage die Bedingungen, die Abwesenheit von Anomalien garantieren, zu entschärfen. Phänomenologische Modelle, die gerade diese Art von Kopplungen beinhalten, sind seit einiger Zeit Mittelpunkt reger Untersuchungen. Mögliche Realisierungen für entsprechende Modelle sind zum Beispiel durch sich schneidende Branen-Modelle in Orientifoldkompaktifizierungen von Typ II Stringtheorien gegeben. Die Vorhersagen der phänomenologischen Untersuchungen dieser Modelle könnten sogar in naher Zukunft in Kollisionsexperimenten nachgeprüft werden, falls nur die Masse des anomalen U(1)-Eichbosons klein genug ist.

Extremal black holes in theories of gravity coupled to abelian gauge fields and neutral scalars, such as those arising in the low-energy description of compactifications of string theory on Calabi-Yau manifolds, exhibit the attractor phenomenon: on the event horizon the scalars settle to values determined by the charges carried by the black hole and independent of the values at infinity. It is so, because on the horizon the energy contained in vector fields acts as an effective potential (the black hole potential), driving the scalars towards its minima. For spherically symmetric black holes in theories where gauge potentials appear in the Lagrangian solely through field strengths, the attractor phenomenon can be alternatively described by a variational principle based on the so-called entropy function, defined as the Legendre transform with respect to electric fields of the Lagrangian density integrated over the horizon. Stationarity conditions for the entropy function then take the form of attractor equations relating the horizon values of the scalars to the black hole charges, while the stationary value itself yields the entropy of the black hole. In this study we examine the relationship between the entropy function and the black hole potential in four-dimensional N=2 supergravity and demonstrate that in the absence of higher-order corrections to the Lagrangian these two notions are equivalent. We also exemplify their practical application by finding a supersymmetric and a non-supersymmetric solution to the attractor equations for a conifold prepotential. Exploiting a connection between four- and five-dimensional black holes we then extend the definition of the entropy function to a class of rotating black holes in five-dimensional N=2 supergravity with cubic prepotentials, to which the original formulation did not apply because of broken spherical symmetry and explicit dependence of the Lagrangian on the gauge potentials in the Chern-Simons term. We also display two types of solutions to the respective attractor equations. The link between four- and five-dimensional black holes allows us further to derive five-dimensional first-order differential flow equations governing the profile of the fields from infinity to the horizon and construct non-supersymmetric solutions in four dimensions by dimensional reduction. Finally, four-dimensional extremal black holes in N=2 supergravity can be also viewed as certain two-dimensional string compactifications with fluxes. Motivated by this fact the recently proposed entropic principle postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes. Invoking the conifold example we find that the entropic principle would favor compactifications that result in infrared-free gauge theories.