Talks of Arun Ram

Talks

Arun Ram

Department of Mathematics
University of Wisconsin-Madison
480 Lincoln Drive
Madison, WI 53706
ram@math.wisc.edu

and

Department of Mathematics and Statistics
University of Melbourne
Parkville VIC 3010 Australia
A.Ram@ms.unimelb.edu.au

I have, too slowly, been coming to the realisation that what I understand in mathematics is far ahead of what I can write up in a polished form and that much of my contribution to the progress of mathematics comes from my lectures. Hopefully, putting as many of these lectures on the web as I can manage will help mathematics move along as quickly as possible. (This is not a complete list. There are some years where I seem to have no records at all, and others for which I have records only of colloquium and invited conference talks.)

Some of this material is based upon work supported by the National Science Foundation under Grant No. 0353038. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

Talks of Arun Ram in 2008

Invited speaker at the International conference on Combinatorics and Representation Theory, Graduate School of Mathematics, Nagoya University, from September 1-5, 2008.
Introduction to the Path Model, Seminar/Introduction, University of Melbourne, 2 July 2008.
Type C Hecke and Temperley-Lieb algebras, Seminar/Introduction, University of Melbourne, 27 June 2008.
A combinatorial formula for Macdonald polynomials, Stanford Combinatorics and Geometry seminar, Stanford University, April 30, 2008.
Abstract: We will explain a common generalization of Littelmann's formula for Weyl characters and Schwer's formula for spherical functions for a p-adic group. These formulas hold for arbitrary Lie type.
Symmetric functions d'après Macdonald, Keynote presentation at the 4th annual Graduate Student Combinatorics Conference, UC Davis, April 12-13, 2008.
Abstract: This talk will be a road map to Macdonald's classic book on Symmetric functions, highlighting the combinatorics, representation theory and geometry coded by symmetric function identities.
Path Models (pdf notes), invited talk at Topics in Combinatorial Representation Theory, MSRI, Berkeley, March 17-21, 2008.
Abstract: Recent years have seen big developments in the theory and applications of path models. The new applications are in understanding the combinatorics of the affine Hecke algebra, spherical functions, and the geometry of points in affine flag varieties. This talk will survey some of these recent results.
Tantalizer algebras, Colloquium University of Utah, March 6, 2008.
Abstract: Abstract: Tantalizer is short for tensor power centralizer. These algebras often come as algebras of diagrams or of tangles, and so working with them requires drawing lots of pictures. Their structure and representation theory contains and immense amount of information about the representation theory of groups and quantum groups of types GL, SO, Sp, and they can be used to construct corresponding link polynomials and 3-manifold invariants. This talk will be a survey of some recent developments in tantalizer algebras.
Path Models, Representation Theory seminar, University of Utah, March 7, 2008.
Abstract: This talk will be a survey of applications of path models: The Weyl character formula, Schubert calculus, spherical functions, normal forms in Chevalley groups, and indexing of points in affine flag varieties and Mirkovic-Vilonen cycles.
Tantalizers, invited talk at University of California Lie Theory Workshop, a conference in honor of Georgia Benkart, University of California, San Diego, February 16-18, 2008.
Abstract: A tensor power centralizer algebra (tantalizer) is the algebra of commuting operators for a Lie group or quantum group action on tensor space. The favourite examples are the group algebra of the symmetric group and the Brauer algebra. This talk will survey some recent work on tantalizers: giving definitions and recent results for affine and graded BMW algebras and some two boundary tantalizers.
Minicourse: Combinatorics of Lie Type, three lectures at the Introductory Workshop on Combinatorial Representation Theory at MSRI, January 22-25, 2008.

Talks of Arun Ram in 2007

Combinatorial Representation Theory 2008-2018, Colloquium, University of Minnesota, November 15, 2007.
Abstract: The 1997 survey article of Barcelo-Ram entitled Combinatorial Representation Theory “defined” the field and set out its structure. In 2007 this field is thriving and vibrant. In Spring 2008 there will be a full semester program at MSRI entitled Combinatorial Representation Theory. Where is the field now? What has happened in the interim 1997-2007? More importantly, what will happen in Combinatorial Representation Theory in 2008-2018?
Generalizing partitions and standard tableaux, combinatorics seminar, University of Minnesota, November 15, 2007.
Abstract: The irreducible representations of the symmetric group are indexed by partitions and bases of these representations are indexed by standard tableaux. The representation theory of the affine Hecke algebras provides a generalization of partitions and standard tableaux. I will explain these combinatorial indexings and how they arise.
Two row partitions and the Temperley-Lieb algebra, Combinatorics seminar, University of Wisconsin, Madison, October 15, 2007.
Abstract: Following a good idea of V. Rittenberg, two boundary diagram algebras are getting more and more attention, with two boundary Temperley-Lieb algebras being a fundamental example. This talk will begin to answer the question: Which Type C affine Hecke algebra representations are two boundary Temperley-Lieb representations and what is a good combinatorial set for indexing these representations?
Boundary diagram algebras, Representation theory seminar, University of Wisconsin, Madison, October 12, 2007.
This talk was a repeat of a talk given at University of Koln on 19 November 2005.
Centers of tantalizers, Representation theory seminar, University of Wisconsin, Madison, September 14, 2007.
Abstract: Many diagram algebras arise as tantalizers. The Schur-Weyl duality makes it possible to steal most of the center of the tantalizer from the corresponding dual object in the duality. I will outline this process and explain how combinatorial results pop out of the picture. This talk is based on joint work with Zajj Daugherty and Rahbar Virk.
Today I feel like a mathematician - personality, music and geometry, The 21st Behrend Memorial Lecture, a public lecture at the University of Melbourne, August 21, 2007.
Abstract: What does it feel like to be a mathematician? Who are the people who discovered and proved the Weil conjectures (one of the great human achievements of the 20th century)? Are they artists, musicians, or scientists? So, what does it feel like to be a mathematician, really?
Combinatorics in affine flag varieties, 6 July 2007; invited talk at GL07, Geometry and Lie Theory, a conference in honor of Gus Lehrer's 60th birthday, University of Sydney, July 2-6 and July 9-13, 2007.
Abstract: This talk is about the combinatorics of indexing points in affine flag varieties. It is possible to make choices so that the points are indexed by a refinement of Littelmann's path model in such a way that the Schubert cell and the Mirkovic-Vilonen slice are easily read off the "path" indexing of the point. From this, the relations for the affine Hecke algebra can be derived, both in the Iwahori-Matsumoto and in the Bernstein generators. If time permits I will discuss the action of the "root operators" on points, and/or the relation to the Kamnitzer and Baumann-Gaussent indexings of Mirkovic-Vilonen cycles.
What is a Weyl group?, Summer Representation Theory seminar, University of Wisconsin-Madison, 14 June 2007.
Level l Fock spaces and the polynomial representation of Cherednik's double affine Hecke algebra,American Institute of Mathematics workshop: Arithmetic harmonic analysis on character and quiver varieties, American Institute of Mathematics, Palo Alto, June 4-8, 2007.
Introduction to Buildings and Combinatorial Representation Theory, American Institute of Mathematics workshop on Buildings and Combinatorial Representation Theory, Palo Alto, March 26, 2007.
Introduction to moment maps on flag varieties, Lie Theory seminar, University of Wisconsin, Madison, 21 March, 2007.

Talks of Arun Ram in 2006

Plenary lecture at the 2006 Fall American Mathematical Society Southeastern Section Meeting, University of Arkansas, Fayetteville, Arkansas, 3-4 November 2006.
Lecture at the workshop Modern Math: An Introduction to 2007-08 Programs at MSRI, at the Society for the Advancement of Chicanos and Native Americans in Science , National Conference, Tampa, Florida, October 24-25, 2006.
Combinatorial Hopf algebras: An outsider's survey, Minicourse at the conference Hopf algebras, Combinatorics and Quantum field Theory, Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany, 25-28 September 2006.
Path models and Chevalley groups, Oberwolfach meeting on Finite groups and representation theory, March 25-31, 2006.
Representations and translation, Special lecture in Quantum groups course, KdV Institut, Amsterdam, March 22, 2006.
Row reduction and loop groups, Lie Theory seminar, University of Wisconsin, Madison, February 28, 2006.
The Schur Hopf algebra, Combinatorics seminar, University of Wisconsin, Madison, February 27, 2006.
Alcove walks and reductive groups over local fields, Lie group and Representation Theory seminar, University of Maryland, February 3, 2006.
In this talk I presented the precise combinatorial construction of the generalized MV cycles by labeled alcove walks.
Examples of groups: Lecture 1 - Reflection groups and braid groups, Lecture 2 - Matrix groups and Lie groups, Special minicourse, University of Rome "La Sapienza", January 23-24, 2006.
These lectures were for advanced undergraduates in mathematics in Italy: introductory lectures on braid groups, reflection groups, matrix groups and Lie groups.
Hecke algebras and spherical functions, Harmonic analysis seminar, University of Rome "La Sapienza", January 18, 2006.

Talks of Arun Ram in 2005

Boundary diagram algebras, Seminar on Transformation groups & mathematical physics, a joint seminar of the Universities of Koln, Hamburg, Bochum, Bremen and Darmstadt, University of Koln, November 19, 2005.
This talk is about diagram algebras which come from the two-boundary braid group (braids with two poles). This is a generalization of recent work (from statistical mechanics) on two-boundary Temperley-Lieb algebras. The generalized setting naturally includes two boundary Hecke algebras and two-boundary BMW algebras. These algebras are like affine Hecke algebras (of type A) and affine BMW algebras except with two poles.
p-compact groups, Oberseminar Geometrie, University of Fribourg, Switzerland, October 26, 2005
This talk was the first time I realised that applying Milnor's construction of the classifying space to the p-compact groups of Clark-Ewing gives the space where path models (such as the Littelmann path models) live.
Random walks, spherical functions and representations, Colloquium, University of Fribourg, Switzerland, October 25, 2005.
p-compact groups, Algebra seminar, University of Rome "La Sapienza", October 20, 2005.
This talk was my first attempt to learn something about p-compact groups.
Diagram algebras as tantalizers, Colloquium, University of Rome "Tor Vergata", October 19, 2005.
This talk was the first time I realized and defined the graded version of the group algebra of the affine braid group which has, as quotients, the graded BMW algebras (also called cyclotomic Nazarov-Wenzl algebras), and the graded Hecke algebras.
Representations of affine Hecke algebras, Algebra seminar, University of Rome "La Sapienza", October 13, 2005.
This talk was a survey on the representations of affine Hecke algebras.
Alcove walks and Iwahori cosets Algebra seminar, University of Rome "La Sapienza", October 6, 2005.
This talk was where I first worked out the generalization of the MV cycles to G/I, in the example SL_2. In other words, coset representatives for the cosets in U^+vI\cap IwI, coset representatives for the cosets in U^+vI\cap IwI, where I is an Iwahori, and v and w are elements of the affine Weyl group.
Picturing Hecke algebras and loop groups, Algebra seminar, University of Rome "La Sapienza", September 29, 2005.
This talk was an attempt to explain the alcove walk method of looking at affine Hecke algebras and loop groups.
Random walks, spherical functions and representations, Colloquium, University of Stuttgart, July 4, 2005.
q-crystals , Invited speaker in the special session in honor of Adriano Garsia at the conference Formal Power Series and Algebraic Combinatorics 2005, June 24-25, 2005.
Commuting elements in diagram algebras, Algebra seminar, University of Wuppertal, June 7, 2005.
Verma crystals, Algebra seminar, University of Lyon 1, May 27, 2005.
Random walks, spherical functions and representations, Colloquium, University of Lyon 1, May 26, 2005.
Walks, crystals and polytopes, Algebra seminar, University of Caen, May 24, 2005.
Random walks, spherical functions and representations, Colloquium, University of Freiburg, May 13, 2005.
Murphy elements in diagram algebras, Plenary speaker at the conference Cellular and diagram algebras and their applications in mathematics and physics, University of Leicester, England, April 3-10, 2005.
Combinatorial Representation Theory, Colloquium, Max-Planck-Institut fur Mathematik, March 24, 2005.
Combiantorial Representation theory II-Crystals, Talk 2 of a lecture series at University of Zaragoza, Spain, February 24, 2005.
Combinatorial Representation theory I-Towers and Centralizers, Talk 1 of a lecture series at University of Zaragoza, Spain, February 22, 2005.
Representations of Reflection groups, Seminar, Bernoulli Centre, EPFL, Lausanne, January 19, 2005.

Talks of Arun Ram in 2004

(12) Algebra seminar, University of Virginia, November 19. 2004

(11) Colloquium, University of Virginia, November 18, 2004.

(10) Colloquium, Michigan Sate University, November 4, 2004.

(9) Distinguished lecture series "The Shoemaker Lectures", University of Toledo, November 1-3, 2004.

(8) Invited speaker and the AMS conference special session on Algebraic Representations and Deformations, Evanston Illinois, October 22-23, 2004.

(7) Algebra seminar, University of Wuppertal, Germany, July 9, 2004.

(6) Plenary speaker at the 11th conference of the International Linear Algebra Society, University of Coimbra, Portugal, July 19-22, 2004.

(5) Lecture series (joint with P. Diaconis) on Representation Theory and its Applications University of Coimbra, Portugal, July 15-16, 2004.

(4) Algebra seminar, University of Illinois, Urbana-Champaign, April 24, 2004.

(3) Algebra seminar, Stanford University, March 29, 2004.

(2) Invited speaker at the Groups and Representations Conference dedicated to the 60th birthday of Gary Seitz March 24 - 27, 2004, University of Oregon, Eugene, Oregon.

(1) Plenary speaker at the International Colloquium on Algebraic Groups and Homogenous Spaces, Tata Institute for Fund. Research, Bombay, India, January 6-14, 2004.

Talks of Arun Ram in 2003

(5) Plenary speaker at the KIAS International Conference on Lie algebra and related topics, Korea Institute for Advanced Study, Seoul Korea, October 20-24, 2003.

(4) Lecture series for the Summer school on the theory of group representations, University of Lisbon, Portugal, July 21-25, 2003.

(3) Plenary speaker at the Nineteenth British Combinatorial Conference, University of Wales, Bangor, Wales, June 29-July 4, 2003.

(2) Invited speaker at the BIRS Workshop Recent Advances in Algebraic and Enumerative Combinatorics, Banff International Research Station, May 3-8, 2003.

(1) Invited speaker at the conference Representations of finite groups, Oberwolfach, Germany, March 23-29, 2003.

Talks of Arun Ram in 2002

(6) Plenary speaker for the 46th Annual conference of the Australian Mathematical Society, Newcastle, Australia, September 30-October 3, 2002.

(5) Geometry seminar at University of Wuppertal, Wuppertal, Germany, July 2, 2002.

(4) Plenary speaker for the Quantum groups day at the XXIV International Colloquium on Group Theortical Methods in Physics, Paris, France, July 15-20, 2002.

(3) Invited speaker at the conference on Computational Lie theory, at the Centre Recherches Mathematiques of the University of Montreal, May 27-June 7, 2002.

(2) Colloquium, University of Massachusetts, Amherst, March 28, 2002.

(1) Plenary speaker, two one hour lectures, at the Mid-Atlantic Algebra Conference, Wake Forest University, March 16-17, 2002.

Talks of Arun Ram in 2001

(15) Invited speaker at the International conference on Algebra and Geometry, Hyderabad, India, December 7-14, 2001.

(14) Colloquium, Institute of Mathematical Sciences, Chennai, Madras, India, December 16, 2001.

(13) Invited speaker, three one hour talks, at the Ramanujan Institute for Advanced Study in Mathematics, University of Madras, India, December 14-15, 2001.

(12) Invited speaker at the conference Combinatorial and Geometric Representation Theory, Seoul National University, Seoul, Korea, October 22-26, 2001.

(11) Invited speaker at the Midwest Lie algebras and related topics conference, De Paul University, October 6-7, 2001.

(10) Invited speaker at the conference Representations of Finite Groups, Oberwolfach, Germany, March 25-31, 2001.

(9) Sandy Green conference, Gregynog, June???, 2001.

(8) Chevalley Seminar, Paris, May???, 2001.

(7) Seminars?? Aarhus, May???, 2001.

(6) Colloquium at Binghamton, April???, 2001.

(5) Seminar, Glasgow, April???, 2001.

(4) Seminar, City University of London, March???, 2001.

(3) Seminar Leicester, March???, 2001.

(2) Colloquium, Warwick, March???, 2001.

(1) Seminar, Isaac Newton Institute, February???, 2001.

Talks of Arun Ram in 2000

(1) Colloquium, University of Oregon, Eugene, March 6, 2000.

Talks of Arun Ram in 1999

(7) Invited speaker at the {\sl KIAS Lie Theory Conference} at the Korea Institute for Advanced Study (KIAS), Seoul, Korea, October 5-8, 1999.

(6) Invited speaker at the conference {\it Quantum groups and knot theory}, at L'Institut de Recherche Math\'ematique Avanc\'ee, Strasbourg, France, September 27-29, 1999.

(5) Invited lecture series at the Korea Institute for Advanced Study (KIAS), Seoul, Korea, June 12-24, 1999.

(4) Tableaux, hyperplanes and representations, plenary talk at the 11th Conference on Formal Power Series and Algebraic Combinatorics, Barcelona, June 7-11, 1999.

(3) Tableaux, hyperplanes and representations, Colloquium, Center for Communications Research, Princeton, May 18, 1999.

(2) Affine braids, quantum groups, and Jantzen filtrations, Invited speaker at the special session on Representations of Lie algebras at the American Math. Society meeting, Buffalo, NY, April 24-25, 1999.

(1) Tableaux, hyperplanes and constructing representations, a lecture series at the Institute of Advanced Study, February 1999.

Talks of Arun Ram in 1998

(10) Combinatorics, representations and vector bundles on flag varieties, Colloquium, Princeton University, December 1998.

(9) Young tableaux, root systems and affine Hecke algebras and A Pieri-Chevalley formula for the K-theory of the flag variety, two one hour invited talks at the workshop on The Interaction of Combinatorics and Representation Theory, Research Institute for Mathematical Sciences, Kyoto University, October 1998.

(8) The fine structure of representations of affine Hecke algebras, 1 hour invited talk at the ICM 1998 Satellite conference on Representations of finite groups and combinatorics, Magdeburg, Germany, August 1998.

(7) Connecting to affine Hecke algebras, 1 hour invited talk at the conference Representations of affine and quantum affine algebras and their applications, Raleigh, North Carolina, May 1998.

(6) Young tableaux in the space age, Haverford-Bryn Mawr Mathematics Colloquium, Haverford College, April 1998.

(5) A group tour of combinatorial representation theory, Colloquium, George Washington University, April 1998.

(4) Young tableaux in the space age and Why are centralizers so stringy?, invited talks at the GWU Combinatorics Day, George Washington University, April 1998.

(3) Modular representation theory for affine Hecke algebras, invited talk in the special session Representation theory of Lie algebras, algebraic groups, and quantum groups, Amer. Math. Soc. conference, Kansas State University, March 1998.

(2) Combinatorics and representations of affine Hecke algebras, Colloquium, Columbia University, February 1998.

(1) Combinatorics and representations of affine Hecke algebras, Colloquium, University of Virginia, January 1998.

Talks of Arun Ram in 1997

(1) Combinatorial representation theory, 1 hour invited talk in the special session Representations of algebras and groups, Amer. Math. Soc--Mexican Math. Soc. Joint meeting, Oaxaca, Mexico, December 1997.

(2) Combinatorics and representations of affine Hecke algebras, Colloquium, Temple Univ., November 1997.

(3) Combinatorics and representations of affine Hecke algebras, Colloquium, Univ. of Illinois--Chicago, November 1997.

(4) Combinatorics and representations of affine Hecke algebras, Colloquium, Univ. of Wisconsin--Madison, October 1997.

(5) Geometry and the combinatorics of affine Hecke algebras, Alperin/Glauberman seminar, Univ. of Chicago, October 1997.

(6) A global formula for the quantum Weyl group, in the special session on Enveloping algebras and Quantum groups, Amer. Math. Soc. conference, Milwaukee, Wisconsin, October 1997.

(7) Representations of affine Hecke algebras, Colloquium, Tata Institute of Fundamental Research, Mumbai, India, August 1997.

(8) Combinatorics and representation theory: Recent results for affine Hecke algebras, plenary address at the l Fifth Australasian Math. Convention, Auckland, New Zealand, July 1997.

(9) Representations of affine Hecke algebras, Colloquium, University of Newcastle, Australia, July 1997.

(10) Combinatorial representation theory, invited speaker in the special session on Combinatorics and Algebra, Mathematical Association of America conference, Logan, Utah, April 1997.

(11) Seminormal representations, affine Hecke algebras, Jucys-Murphy elements and the Shi arrangement, invited speaker at the Workshop in Representation theory and symmetric functions, MSRI, Berkeley, April 1997.

(12) Another look at Hoefsmit's representations, Colloquium, Univ. of British Columbia, Vancouver, February 1997.

(13) Iwahori-Hecke algebras of type A, bitraces and symmetric functions, invited talk at the special session in algebraic combinatorics, AMS-MAA joint meetings, San Diego, January 1997.

Talks of Arun Ram in 1996

(3) Hyperplanes, Hecke algebras and combinatorics, Colloquium, North Carolina State University, November 1996.

(2) A construction in combinatorial representation theory, Colloquium, University of Georgia, Athens, October 1996.

(1) Quantum groups, series of 5 one hour lectures, Workshop on Algebra, Geometry and Topology, Australian National University, Canberra, January 1996.

Talks of Arun Ram in 1995

(7) Quantum groups, R-matrices, and centralizer algebras, one hour invited talk, Australian Lie Groups Conference '95, University of Adelaide, November 1995.

(6) A construction in combinatorial representation theory, Joint colloquium of University of Sydney and University of New South Wales, November 1995.

(5) On a (traditionally complicated, but actually trivial) piece of combinatorial representation theory, Colloquium, University of Melbourne, September 1995.

(4) An elementary approach to the representations of Iwahori-Hecke algebras, Colloquium, University of Wisconsin--Milwaukee, April 1995.

(3) Invited speaker in special session on Lie theory, Amer. Math. Society meeting in Chicago, Illinois, March 1995.

(2) Representations and characters of Iwahori-Hecke algebras, Colloquium, Michigan State University, January 1995.

(1) Representations and characters of Iwahori-Hecke algebras, Colloquium, Notre Dame University, January 1995.

Talks of Arun Ram in 1994

(3) Representations and characters of Iwahori-Hecke algebras Colloquium, Binghamton University, December 1994.

(2) Representations of Iwahori-Hecke algebras and centralizer algebras, Invited speaker, one-hour talk, Midwest group theory conference, Madison, Wisconsin, October 1994.

(1) Centralizer algebras+Path algebras+Quasitriangular Hopf algebras=Irreducible representations, Invited speaker, one-hour talk, Third conference in algebraic combinatorics at Ann Arbor, Michigan, June 1994.

Talks of Arun Ram in 1993

(3) Orthogonality of characters, regular representations and Weyl group symmetric functions, Invited talk in special session on algebraic combinatorics, SIAM annual meeting, Philadelphia, July 1993.

(2) On the second orthogonality relation for characters of the Brauer algebras, Invited speaker at E'cole internationale de combinatoire de Bordeaux, June 1993.

(1) Braids, quantum groups, and centralizer algebras, Colloquium, University of Wisconsin-Parkside, February 1993.

Talks of Arun Ram in 1992

(2) Weyl group symmetric functions and the representation theory of Lie algebras, 4th conference Formal Power series and Algebraic combinatorics, Univ. de Quebec a Montreal, June 1992.

(1) Character classes in Hecke algebras, Colloquium, Virginia Polytechnic Institute, May 1992.

Talks of Arun Ram in 1991

(2) Quantum groups and the characters of the Hecke algebras, Colloquim, Trinity College, Dublin, Ireland, April 1991.

(1) Characters of Hecke algebras, Colloquim, Universitat Basel, Switzerland, May 1991.

Talks of Arun Ram in 1990

(2) A Frobenius formula for the characters of the Hecke algebras, Jones/Grunbaum seminar, Univ. of Calif., Berkeley, October 1990.

(1) Frobenius formulas for the characters of the Hecke algebras and Brauer's centralizer algebras, Colloquium, Univ. of Wisconsin, Madison, September 1990.

Talks of Arun Ram in 1989

(1) Matrix units for the Brauer algebras, Colloquium, New Mexico State Univ., April 1989.