 |
 |
We are writing to announce the workshop, Yangians and Quantum Loop Algebras, to be held May 5-9th, in the vicinity of Austin, TX. The workshop will be led by Valerio Toledano Laredo and Sachin Gautam. I would be grateful if you could forward this email to Ph.D. students and recent Ph.D's who might be interested in applying. We are accepting applications until Friday, February 7th. The website for the workshop is: http://www.ma.utexas.edu/users/djordan/workshop.html Thanks! David Ben-Zvi and David Jordan What and when The week of May 5th-9th, we will be hosting a five-day workshop near Austin, TX for young researchers focusing on emerging algebraic aspects of quantum loop algebras, their representation theory, and their applications to solvable lattice models. The workshop will be led by Valerio Toledano Laredo and Sachin Gautam. Scientific program Yangians and quantum loop algebras are two classes of infinite–dimensional quantum groups associated to a complex semisimple Lie algebra. They were first discovered in the mid–80s as symmetries of solvable models in Quantum Statistical Mechanics, specifically the Heisenberg XXX and XXZ spin chains. They have since appeared in a number of different contexts: Nakajima quiver varities, enumerative geometry, 4 and 5–dimensional supersymmetric gauge theories, scattering amplitudes to name a few. The focus of this workshop will be on the algebraic aspects of these quantum groups, and their applications to solvable lattice models. The goal will be to familiarize the participants with the basics of these models (Yang–Baxter equations, Baxter’s transfer matrix formalism, Bethe Ansatz) and to explain how the Yangian and quantum loop algebra appear naturally. We will then cover their representation theory in some detail, and explain that their finite– dimensional representations form a meromorphic braided tensor category. Finally, we will review some of the recent developments in this area, in particular the construction of a transcendental tensor equivalence between the two representation categories using abelian difference equations. Participants should plan to each give a one-hour talk at the workshop. Topics for talks will be assigned by Valerio and Sachin, together with the organizers, based on particpant's background and interests. The list of topics to be covered includes: Vertex models, Bethe Ansatz, Yangians and quantum loop algebras, affine Lie algebras, Kac-Moody and loop presentations for quantum affine algebras, RTT and loop presentations for Yangians, their finite dimensional representations, meromorphic braided tensor categories, R-matrices for quantum affine algebra and Yangian, quantum KZ equations, trigonometric connections, Drinfeld's degeneration, difference equations, KZ functors. A more complete list, with references, can be found on the website. Accomodation and travel Lodging and food will be provided near Austin in shared accommodation. Depending on funding, it may be possible to provide partial travel reimbursements, but participants should seek this primarily from their advisors or departments. Who should apply, how to apply Our ideal mix of participants will include both Ph.D students and recent Ph.D's. A background in quantum groups, affine Lie algebras, or representation theory more broadly is helpful but not required. Interested applicants should start by filling out the form linked on the website. We are accepting applications until February 7th. Contact us Please feel free to contact organizing commitee members David Jordan, David Ben-Zvi, Iordan Ganev, or Lee Cohn (emails available on the website) with any questions! =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- This message was sent to you via the Geometry List, which announces conferences in geometry and closely related areas to over 1200 mathematicians worldwide. At http://listserv.utk.edu/archives/geometry.html there are many functions available, including checking the archives since November 2005, changing your e-mail address or preferences, and joining/leaving the list. If you have problems that cannot be resolved at this website, send a message to [log in to unmask] Before sending an announcement, please carefully read the following. Any announcements that are *not* about conferences (e.g. those about jobs, journals, books, etc.) will be rejected by the moderator without comment. To announce a geometry or closely related conference, send the announcement (including a conference web site if possible) to [log in to unmask] The moderator cannot edit your message; list members will receive the announcement as an e-mail from you EXACTLY as you submitted it. For example, if your submission starts with "Please post this on the geometry list" then your conference announcement will also begin with that statement. In order to keep down the volume of e-mail, only TWO announcements per conference will be approved by the moderator. The "subject" of your message should include the name of the conference and the number (first or second) of the announcement, e.g. Gauss Memorial Lectures in Geometry: Second Announcement. Please check that your announcement (especially the website) is correct. Corrections will be approved only in the most critical situations, e.g. if corrected information is not available on the website. If you send a submission from an e-mail address that is not subscribed to the geometry list then you will be sent an e-mail asking for confirmation. This feature is designed to thwart the hundreds of machine-generated spam that are sent to the list and would otherwise have to be manually blocked by the moderator. The Geometry List is sponsored and maintained by the Mathematics Department, The University of Tennessee, Knoxville.