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-<html>
+====== Student-Run/Informal ADM Seminar ======
-<p><h1>Student Discrete Math Seminar</h1></p>
-<p><h2><a name="Logistics"></a>Logistics</h2></p>
+This seminar will resume in Winter 2025. It is currently organized by [[https://jonerickson.org/|Jon Erickson]], Lisa Johnston, and [[https://sites.google.com/ucdavis.edu/soyeon-kim/home|Soyeon Kim]]. We intend for the seminar to be an informal introduction to topics of broad interest in algebra and discrete math, primarily aimed at people without lots of background in those areas. First and second year grad students who are interested in ADM are especially welcome!
-<p>Information can be found at <a href="http://www.math.ucdavis.edu/courses.htm">Math department courses webpage</a> and the UC Davis Math Dept's <a href="http://www.math.ucdavis.edu/research/seminars?when=future.htm">Seminar Page</a>.<br /><br /></p>
-<p>Please join us for the Student Discrete Math
+===== Logistics =====
-Seminar. Although we don't have pizza, the talks are always interesting.
-Talk to the organizers if you have any questions or would like to speak at the seminar.</p>
+The seminar will meet weekly on Thursdays from 4:10-5pm in MSB 3106. We will have snacks! Talk to the organizers if you have any questions or would like to speak at the seminar.
-<p><h2>Topic Ideas</h2></p>
-<p>The most commonly asked question, especially for new graduate students, is: "I would
+===== Tentative List of Talks =====
+Note: The organizers are planning to give talks for the first several weeks, but anyone is welcome to speak. Talks which have two parts should be independent enough that anyone attending the second talk (but not the first) can still follow along and learn.
+  * Week of 1/13: Soyeon Kim, Cluster algebras and plabic graphs
+  * Week of 1/20: Soyeon Kim, Cluster algebras and plabic graphs
+  * Week of 1/27: Lisa Johnston, {{ ::a_crash_course_on_symmetric_functions_and_young_tableaux_pt_1.pdf | A crash course on symmetric functions and Young tableaux Pt.1 }}
+  * Week of 2/03: Lisa Johnston, {{ ::symmetric_functions_tableaux_.pdf | A crash course on symmetric functions and Young tableaux Pt.2}}
+  * Week of 2/10: Jon Erickson, Grassmannians and flag manifolds
+  * Week of 2/17: Jon Erickson, Grassmannians and flag manifolds
+  * Week of 2/24: Timothy Paczynski, Toric varieties
+  * Week of 3/3: Anouk Brose, Intro to polytopes, lattice polytopes and Ehrhart Theory
+  * Week of 3/10: Brittney Marsters, TBD
+===== Topic Ideas =====
+The most commonly asked question, especially for new graduate students, is: "I would
 like to speak, but I don't know what to talk about!  What can I give a talk on?"
-Below we have some suggestions.  Disclaimers: This list does not in any way attempt to cover
-all of Discrete Mathematics, but instead focuses on research areas that are more
+The list is a work in progress - check back soon for updates. Suggestions are welcome!
-related to UC Davis specialties.  In fact, the list does not even exhaust all of the topics
-that UC Davis <i>does</i> specialize in, but only what we happened to think of at the time.
-You are encouraged to seek out other topics and papers.  Although there has been an attempt
-to organize and categorize, many papers and books belong in several categories, so take it
-all with several grains of salt.</p>
-<p>The list is a work in progress - check back often for updates.</p>
-<h2><ul></h2>
-<p> <h4>New Suggestions (Spring 2011)</h4></p>
-<h2><ul></h2>
-<p> <li>The papers listed here: <a href="http://www.math.ucdavis.edu/~deloera/forstudents.htm">http://www.math.ucdavis.edu/~deloera/forstudents.htm</a> </li></p>
-<p> <li>Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves. Crystal graphs and $q$-analogues of weight multiplicities for the root system $A_n$. Lett. Math. Phys. 35 (1995), no. 4, 359â€“374. </li></p>
-<p> <li>Brenti, Francesco; Fomin, Sergey; Postnikov, Alexander. Mixed Bruhat operators and Yang-Baxter equations for Weyl groups. Internat. Math. Res. Notices 1999, no. 8, 419â€“441. </li></p>
-<p> <li>Jason Bandlow, Anne Schilling, Mike Zabrocki. The Murnaghan-Nakayama rule for k-Schur functions. Journal of Combinatorial Theory, Series A, 118(5) (2011) 1588-1607. </li></p>
-<h2><ul></h2>
-<p> <h4>Quantum Groups and Representation Theory, Crystals</h4></p>
-<h3> <ul></h3>
-<p>  <li> Littelmann, Peter, A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras. Invent. Math. 116 (1994), no. 1-3, 329--346 MR1253196 </li></p>
-<p>  <li> Cristian Lenart, Alexander Postnikov, A Combinatorial Model for Crystals of Kac-Moody Algebras
-<a href="http://arxiv.org/abs/math/0502147v4">http://arxiv.org/abs/math/0502147v4</a> </li></p>
-<p>  <li> Arun Ram, Alcove walks, Hecke algebras, Spherical functions, crystals and column strict tableaux, Pure and Applied Mathematics Quarterly  2 no. 4 (Special Issue: In honor of Robert MacPherson, Part 2 of 3) (2006) 963-1013. </li></p>
-<p>  <li> John Stembridge, A Local Characterization of Simply-Laced Crystals, <a href="http://www.math.lsa.umich.edu/~jrs/papers/xtal.ps.gz">http://www.math.lsa.umich.edu/~jrs/papers/xtal.ps.gz</a> </li></p>
-<p>  <li> Masaki Kashiwara, On Crystal Bases </li></p>
-<p> </ul></p>
-<p> <h4> RSK and related algorithms </h4></p>
-<h3> <ul></h3>
-<p>  <li> Edelmann and Greene, Balanced Tableaux </li></p>
-<p>  <li> Sarah Mason, A Decomposition of Schur functions and an analogue of the RSK Algorithm </li></p>
-<p> </ul></p>
-<p> <h4> Books </h4></p>
-<h3> <ul></h3>
-<p>  <li> Hong and Kang, Introduction to Quantum Groups and Crystal Bases </li></p>
-<p>  <li> Fulton and Harris, Representation Theory</li></p>
-<p>  <li> Sagan, The Symmetric Group</li></p>
-<p>  <li> Bjorner and Brenti, Combinatorics of Coxeter Groups</li></p>
-<p>  <li> Humphreys, Reflection Groups and Coxeter Groups</li></p>
-<p>  <li>Humphreys, Lie Algebras</li></p>
-<p>  <li> Bump, Lie Groups</li></p>
-<p>  <li> Erdmann, Introduction to Lie Algebras</li></p>
-<p>  <li> Fulton, Young Tableaux</li></p>
-<p> </ul></p>
-<p> <h4> Finally, perhaps your best resource is older grad students: </h4></p>
-<p>The following is an old listing of topics.  We'll leave it up until we finish the new, more organized list.</p>
-<p><ul>
-  <li>the Edelmann-Greene paper on what we now call Edelmann-Greene
-insertion (actually maybe some of what i'm (Alex Woo) thinking about is
-actually in the Billey-Jockhush-Stanley paper), </li>
-  <li>the Billey-Warrington paper on 321-hexagon-avoiding permutations.
-Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations; <a
- href="http://arxiv.org/abs/math.CO/0005052">
-<a href="http://arxiv.org/abs/math.CO/0005052">http://arxiv.org/abs/math.CO/0005052</a> </a></li>
-  <li>There is an extensive list of papers at the lower part of the
-webpage <a
- href="http://www.math.ucdavis.edu/%7Evazirani/S05/KL.details.html">
-<a href="http://www.math.ucdavis.edu/~vazirani/S05/KL.details.html">http://www.math.ucdavis.edu/~vazirani/S05/KL.details.html</a> </a></li>
-  <li>other interesting papers might be Sarah Mason's recent work on a
-different RSK type algorithm related to nonsymmetric Schur functions.
-Or some papers on Key polynomials. </li>
-  <li>Kevin Purbhoo's paper on root games </li>
-  <li>Almost any section of Macdonald's book. You might also look at
-Fulton's book or Jim Haglund's new book. There are several papers on
-crystal graphs I can also suggest (for instance, in connection to the
-Littlewood-Richardson rule). <br>
-Below are listed several papers related to the saturation
-conjecture/theorem. (In a slightly weird format from cutting/pasting
-from a bibtex file.) In particular there are several papers involving
-polytopes, honeycombs, Littelmann paths, galleries, and buildings. <br>
-&nbsp;</li>
-  <li>Arkady Berenstein, Andrei
-Zelevinsky "<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/bz.9912012.pdf">Tensor
-product multiplicities, canonical bases and totally positive varieties</a>"
-<li>    <a href="http://arxiv.org/abs/math.RT/9912012">math.RT/9912012</a>&nbsp;
-( Invent. Math.&nbsp; 143&nbsp; (2001),&nbsp; no. 1,
---128.)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br>
-&nbsp;&nbsp;&nbsp; [We obtain a family of explicit "polyhedral"
-combinatorial expressions for multiplicities in the tensor product of
-two simple finite-dimensional modules over a complex semisimple Lie
-algebra.&nbsp; Our answers use a new combinatorial concept of
-$\ii$-trails which resemble Littelmann's paths but seem to be more
-tractable.&nbsp; A remarkable observation by G. Lusztig notes that
-combinatorics of the canonical basis is closely related to geometry of
-the totally positive varieties. We formulate this relationship in terms of two mutually inverse transformations:&nbsp;
-"tropicalization" and "geometric lifting."]</li>
-  <li>Anders S. Buch&nbsp; "<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/buch.9810180.pdf">The
-saturation conjecture (after A. Knutson and T. Tao)</a>"<br>
-math.CO/<a href="http://arxiv.org/abs/math.CO/9810180">9810180 </a>(With
-an appendix by William Fulton. Enseign. Math. (2) 46 (2000), no. 1-2,
---60. ) [A nice exposition of the
-hive model and Knutson-Tao's proof of the saturation conjecture (in
-type A).]</li>
-  <li>Joel Kamnitzer&nbsp; "<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/kamnitzer.mvpolytopes.pdf">Mirkovic-Vilonen
-cycles and polytopes</a>"<br>
-math.AG/<a href="http://arxiv.org/abs/math.AG/0501365">0501365</a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [We give an explicit
-description of the Mirkovic-Vilonen cycles on the affine Grassmannian
-for arbitrary complex reductive groups. We also give a combinatorial
-characterization of the MV polytopes. We prove that a polytope is an MV
-polytope if and only if it a lattice polytope whose defining<br>
-hyperplanes are parallel to those of the Weyl polytopes and whose
--faces are rank 2 MV polytopes. As an application, we give a bijection
-between Lusztig's canonical basis and the set of MV polytopes.]</li>
-  <li>M. Kapovich. "<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/kapovich.icm1.pdf">Generalized
-triangle inequalities and their applications</a>",
-- Madrid, August 22-30, 2006. Eds. Marta Sanz-Sol&eacute;, Javier Soria,
-Juan L. Varona, Joan Verdera. Vol. 2, p. 719-742.
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [survey article.
-applications to decomposing tensor products of irreducible
-representations and the saturation theorem in types beyond A.]<br>
-</li>
-  <li>Allen Knutson, Terence
-Tao&nbsp; "<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/knutson.tao.9807160.pdf">The
-honeycomb model of GL(n) tensor products I: proof of the saturation
-conjecture</a>"
-math.RT/<a href="http://arxiv.org/abs/math.RT/9807160">9807160</a>&nbsp;
-( J. Amer. Math. Soc.&nbsp; 12&nbsp; (1999),&nbsp; no. 4, 1055--1090. )<br>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [We introduce the honeycomb
-model of BZ polytopes, which calculate Littlewood-Richardson
-coefficients, the tensor product rule for GL(n).&nbsp; A particularly
-well-behaved honeycomb is necessarily integral, which proves the
-"saturation conjecture", extending results of Klyachko to give a
-complete
-answer to which L-R coefficients are positive. This in turn has as
-a&nbsp; consequence Horn's conjecture from 1962 characterizing the
-spectrum of the sum of two Hermitian matrices.&nbsp; ]&nbsp;</li>
-  <li>Sophie Morier-Genoud's thesis:
-"<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/morier-genoud.pdf">Relevement
-Geometrique de L'involution de Schutzenberger et Applications</a>"
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [in French]<a class="new" href="http://galois.math.ucdavis.edu/AboutDept/StudentDiscreteSeminar/createform?page=in%20French" title="create this page">?</a>
-&nbsp;</li>
-  <li>Arun Ram&nbsp; "<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/ram.alcove_walk.pdf">Alcove
-walks, Hecke algebras, spherical functions, crystals and column strict
-tableaux</a>"
-math.RT/<a href="http://arxiv.org/abs/math.RT/0601343">0601343</a>&nbsp;
-(Pure and Applied Mathematics Quarterly. Special Issue: In honor of
-Robert MacPherson.&nbsp; Vol 2. (2006) 135-183.)
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [This paper makes precise
-the close connection between the affine
-Hecke algebra, the path model, and the theory of crystals. Section 2 is
-a
-basic pictorial exposition of Weyl groups and affine Weyl groups and
-Section 5
-is an exposition of the theory of (a) symmetric functions, (b) crystals
-and
-(c) the path model. Sections 3 and 4 give an exposition of the affine
-Hecke
-algebra and recent results regarding the combinatorics of spherical
-functions
-on p-adic groups (Hall-Littlewood polynomials). The $q$-analogue of the
-theory
-of crystals developed in Section 4 specializes to the path model
-version of
-the ``classical'' crystal theory. The connection to the affine Hecke
-algebra
-and the approach to spherical functions for a $p$-adic group in
-Nelsen-Ram was
-made concrete by C. Schwer who told me that ``the periodic Hecke module<br>
-encodes the positively folded galleries'' of Gaussent-Littelmann. This
-paper
-is a further development of this point of view.]</li>
-  <li>Guy Rousseau :&nbsp; "<a
- href="http://www.math.ucdavis.edu/%7Evazirani/AIM/Reading/rousseau.pdf">Euclidean
-buildings</a>"
-Lecture notes from Summer School 2004: Non-positively curved
-geometries, discrete groups and rigidities
-    <a
- href="http://www-fourier.ujf-grenoble.fr/ECOLETE/ecole2004/Rousseau.pdf">
-<a href="http://www-fourier.ujf-grenoble.fr/ECOLETE/ecole2004/Rousseau.pdf">http://www-fourier.ujf-grenoble.fr/ECOLETE/ecole2004/Rousseau.pdf</a></a><br>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [Introduction to
-buildings.&nbsp; All basic definitions can be found here.]
-&nbsp;</li>
-  <li>Arkady Berenstein, David Kazhdan<br>
-Lecture notes on Geometric Crystals and their combinatorial analogues<br>
-math.QA/<a href="http://arxiv.org/abs/math.QA/0610567">0610567</a><br>
-&nbsp;</li>
-  <li>A path model for geodesics in Euclidean buildings and its
-applications to representation theory, Michael Kapovich and John J.
-Millson, arXiv:math.RT/0411182 </li>
-  <li>{Gaussent, S. and Littelmann, P.}, {L{S} galleries, the path
-model, and {MV} cycles}, {Duke Math. J.}, {Duke Mathematical Journal},
-VOLUME {127}, YEAR {2005}, PAGES {35--88}, </li>
-  <li>{Littelmann, Peter}, {The path model for representations of
-symmetrizable {K}ac-{M}oody algebras}, BOOKTITLE = {Proceedings of the
-International Congress of Mathematicians, Vol.\ 1, 2 (Z\"urich, 1994)},
-PAGES = {298--308}, PUBLISHER = {Birkh\"auser}, YEAR = {1995}, </li>
-  <li>{Littelmann, Peter}, {Paths and root operators in representation
-theory}, {Ann. of Math. (2)}, VOLUME = {142}, YEAR = {1995}, PAGES =
-{499--525}, </li>
-  <li>{Berenstein, Arkady and Zelevinsky, Andrei}, {Canonical bases for
-the quantum group of type {$A\sb r$} and piecewise-linear
-combinatorics}, {Duke Math. J.}, VOLUME = {82}, YEAR = {1996}, PAGES =
-{473--502}, </li>
-  <li>{Berenstein, A. D. and Zelevinsky, A. V.}, {Tensor product
-multiplicities and convex polytopes in partition space}, {J. Geom.
-Phys.}, VOLUME = {5}, YEAR = {1988}, PAGES = {453--472}, </li>
-  <li>Galleries, Hall-Littlewood polynomials and structure constants of
-the spherical Hecke algebra, {Christoph Schwer},
-{arXiv:math.CO/0506287} </li>
-  <li>{De Loera, Jes{\'u}s A. and McAllister, Tyrrell B.}, {Vertices of
-{G}elfand-{T}setlin polytopes}, {Discrete Comput. Geom.}, VOLUME =
-{32}, YEAR = {2004}, PAGES = {459--470}, </li>
-  <li>Knutson, Allen and Tao, Terence and Woodward, Christopher, A
-positive proof of the {L}ittlewood-{R}ichardson rule using the
-octahedron recurrence, {Electron. J. Combin.}, VOLUME = {11}, YEAR =
-{2004}, </li>
-  <li>Knutson, Allen and Tao, Terence, {The honeycomb model of {${\rm
-GL}\sb n({\bf C})$} tensor products. {I}. {P}roof of the saturation
-conjecture}, {J. Amer. Math. Soc.}, VOLUME = {12}, YEAR = {1999}, PAGES
-= {1055--1090}, </li>
-  <li>Knutson, Allen and Tao, Terence and Woodward, Christopher, {The
-honeycomb model of {${\rm GL}\sb n(\mathbb C)$} tensor products. {II}.
-{P}uzzles determine facets of the {L}ittlewood-{R}ichardson cone}, {J.
-Amer. Math. Soc.}, VOLUME = {17}, YEAR = {2004}, PAGES = {19--48
-(electronic)}, </li>
-  <li>Knutson, Allen and Tao, Terence , {Honeycombs and sums of
-{H}ermitian matrices}, {Notices Amer. Math. Soc.}, VOLUME = {48}, YEAR
-= {2001}, PAGES = {175--186}, </li>
-  <li>Buch, Anders Skovsted, {The saturation conjecture (after {A}.\
-{K}nutson and {T}.\ {T}ao)}, {With an appendix by William Fulton},
-{Enseign. Math. (2)}, VOLUME = {46}, YEAR = {2000}, PAGES = {43--60}, </li>
-  <li>&nbsp;<!--
-  <li> Macdonald ``Symmetric functions and orthogonal
-polynomials,''&nbsp; <span style="color: rgb(0, 0, 0);">QA212.M33</span>
-  </li>
-  <li> Koornwinder ``Askey-Wilson polynomials for root systems of type
-$BC$,'' QA353.H9 H97 &nbsp; &nbsp;&nbsp;
-<br>
- Hypergeometric functions on
-domains of positivity, Jack polynomials, and
-applications&nbsp;&nbsp;&nbsp;&nbsp;
-<br>
-(Tampa, FL, 1991), 189--204, Contemp. Math., 138, Amer. Math. Soc.,
-Providence, RI, 1992.
-  </li>
-  <li> Kirillov ``<a
- href="http://www.math.ucdavis.edu/%7Evazirani/RFG/kirillov.pdf">Lectures
-on affine Hecke algebras and Macdonald's conjectures</a>,''</li>
-  <li>Charles Dunkl and Yuan Xu&nbsp;&nbsp; "Orthogonal polynomials of
-several variables."<span style="color: rgb(0, 0, 0);">&nbsp;&nbsp;
-QA404.5.D86</span>&nbsp;&nbsp;&nbsp;
-<br>
- <span
- style="color: rgb(0, 0, 0);">Encyclopedia of Mathematics and its
-Applications, 81.
-Cambridge University Press, Cambridge, 2001.&nbsp;</span><span
- style="color: rgb(0, 0, 0);">&nbsp;&nbsp;&nbsp; <br>
-    </span></li>
-<li>
-Szeg&#337; ``Orthogonal Polynomials,''
-              ( Colloquium publications (American Mathematical Society) ; v. 23)
-<br> Shields Library QA404.5 .S9
-</li>
-<li>
-Andrews, Askey, Roy ``Special functions,"
-              ( Encyclopedia of mathematics and its applications ; v. 71)
-<br> Shields Library QA351 .A74
-</li>
---></li>
-  <li>
-Regular triangulations and the secondary polytope - a good source is
-chapter 7 of the Gelfand-Kapranoz-Zelevinsky book</li>
-</ul></p>
-<p>Further suggestions are welcome!
-</p>
-</html>

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