[McNinch-web]Tag: math2019-06-02T10:22:24-0400two talks in the NIU mathematics department ColloquiumGeorge McNinchgeorge.mcninch@tufts.edu2019-03-23T11:00:00-0400<p>I give two talks at the <a href="http://www.math.niu.edu/colloq/">Northern Illinois University mathematics colloquium</a>.</p><p>Here are the abstracts, and links for the slides (as pdf documents):</p><ul><li><p><strong>Group cohomology and Levi decompositions for linear groups</strong> (Mar 21)</p><p><em>Abstract</em>: If G is a linear algebraic group over a field F, we
describe what the Hochschild cohomology of G with coefficients in
linear representations of G says about those algebraic groups
which are extensions of G by connected unipotent algebraic groups
over F. If G is reductive and if F has characteristic zero -- say,
if F is the field of complex numbers -- one knows that every such
extension is trivial. But if F has positive characteristic, there
are non-trivial extensions -- i.e. there are linear groups with no
Levi decomposition. The talk will give details and examples about
these notions and results.</p><p>Here are <a href="assets/slides/2019-03---NIU--Talk-1--transparencies.pdf">the slides</a></p></li></ul><ul><li><p><strong>Some tools for the study of reductive groups over local fields</strong> (Mar 22)</p><p><em>Abstract</em>: Let K be a local field -- i.e. the field of fractions of a
complete discrete valuation ring A. The study of linear algebraic
groups G over such fields K has applications in number theory and
algebraic geometry. Some reductive groups (“split groups”) have
models over A which are reductive. But e.g. if G does not become
split upon base change with any unramified extension of K, it can
happen that G has no reductive model. Our interest here is in an
interesting family of models for G -- the so-called parahoric
group schemes P. If k denotes the residue field of A, then by
“base-change”, P determines a linear algebraic group P_k over k.
When P is not reductive, we investigate the question: does P_k
have a Levi decomposition (as in the first talk)? This second
talk will include a good bit of example-oriented background
discussion.</p><p>Here are <a href="assets/slides/2019-03---NIU--Talk-1--transparencies.pdf">the slides</a>.</p></li></ul>Dave Richeson gives the Martin Guterman Undergraduate Lecture at TuftsGeorge McNinchgeorge.mcninch@tufts.edu2019-03-11T18:00:00-0400<p><a href="https://divisbyzero.com/">Dave Richeson</a> -- <a href="https://www.dickinson.edu/homepage/117/mathematics">Professor of Mathematics
at Dickinson
College</a> --
gave the <a href="http://math.tufts.edu/seminars/lecturesGuterman.htm">Martin Guterman Undergraduate
Lecture</a>. He
spoke about <em>Tales of Impossibility</em>.</p><p><img src="assets/images/2019-03--Guterman-Lectures.jpg" alt="image" title="flier" /></p>Workshop for Jens Carsten Jantzen’s 70th birthdayGeorge McNinchgeorge.mcninch@tufts.edu2018-11-25T08:00:00-0500<p>I gave one of the lectures at the workshop on <a href="https://www.mpim-bonn.mpg.de/node/8209"><em>Algebraic Groups, Lie
Algebras and their
Representations</em></a> held at the
<a href="https://www.mpim-bonn.mpg.de">Max Planck Institute</a> (Bonn, Germany)
to celebrate the 70th birthday of <a href="https://wikipedia.org/wiki/Jens_Carsten_Jantzen">Jens Carsten
Jantzen</a>.</p><p><img src="assets/images/2018-11-Poster-Jantzen70.jpg" alt="image" /></p>Southeast Lie Theory meeting at the University of Georgia (Athens)George McNinchgeorge.mcninch@tufts.edu2018-06-14T08:00:00-0400<p>I gave a talk on <em>Reductive subgroup schemes of a parahoric group
scheme</em> at the 10th annual <a href="https://www.math.lsu.edu/~pramod/selie/10/">Southeast Lie Theory
workshop</a> at the
University of Georgia (Athens) during June 10–12, 2018.</p><p>Here are the <a href="assets/slides/2018-05---Athens---transparencies.pdf">slides for my talk</a>.</p><p>And here is a conference photo (I seem to be ’way at the top of the stairs!):</p><p><img src="assets/images/2018-06-SELieConfPic.jpg" alt="conference photo" title="photo" /></p>Lyon meeting: Groupes algébriques et géométrisation du programme de LanglandsGeorge McNinchgeorge.mcninch@tufts.edu2018-05-30T08:00:00-0400<p>I attended some workshops during the <a href="https://geolang.sciencesconf.org/">Trimestre
thématique</a> on <em>Groupes algébriques
et géométrisation du programme de Langlands</em> in Lyon (France).</p><p>During this time, I followed the <em>Mini-cours sur la correspondence de
Langlands locale pour les corps locaux d'égale caractéristique,
d'après Genestier-Lafforgue</em> given by <a href="https://web.math.princeton.edu/~smorel/">Sophie
Morel</a> and <a href="https://webusers.imj-prg.fr/~benoit.stroh/">Benoît
Stroh</a>.</p><p>Following the minicourse, there was a conference during May 22-25, 2018:</p><p><img src="assets/images/2018-05-Lyon-poster-small.jpg" alt="" /></p><p>In this conference, I gave a lecture on <em>Reductive subgroup schemes of
a parahoric group scheme</em>.</p>Special Session in AMS sectional meeting at Northeastern UnivGeorge McNinchgeorge.mcninch@tufts.edu2018-04-23T08:00:00-0400<p>The Spring Eastern Sectional Meeting of the AMS
was held at Northeastern University (Boston, MA)
April 21-22, 2018.</p><p>At this meeting, there was a special session on <a href="http://www.ams.org/meetings/sectional/2252_program_ss15.html#title">Combinatorial Aspects
of Nilpotent
Orbits</a>
organized by Anthony Iarrobino (Northeastern University), Leila
Khatami (Union College) and Juliana Tymoczko (Smith College).</p><p>In this session, I gave a presentation on <em>Centralizers of nilpotent
elements</em>; here are the <a href="assets/slides/2018-04---Northeastern---nilpotent-centralizers---transparencies.pdf">slides for my
talk</a>.</p>MSRI program on Representations of Finite and Algebraic GroupsGeorge McNinchgeorge.mcninch@tufts.edu2018-04-14T08:00:00-0400<p>I attended the <a href="http://www.msri.org/web/cms">MSRI</a> program
<a href="http://www.msri.org/workshops/820">Representations of Finite and Algebraic
Groups</a> Apr 9 - 13, 2018, organized
by Robert Guralnick (University of Southern California), Alexander
Kleshchev (University of Oregon), Gunter Malle (Universität
Kaiserslautern), Gabriel Navarro (University of Valencia), and Pham
Tiep (Rutgers University)</p><p><img src="assets/images/2018-MSRI-building.jpg" alt="image" /></p>Ken Ono delivers Norbert Wiener Lectures at Tufts UniversityGeorge McNinchgeorge.mcninch@tufts.edu2017-12-09T12:00:00-0500<p><a href="http://www.mathcs.emory.edu/~ono/">Ken Ono (Asa Griggs Candler Professor, Department of Math and CS,
Emory University)</a> gave the <a href="http://math.tufts.edu/seminars/lecturesWiener.htm">Wiener
Lectures in the Tufts University Math
Department</a> in
December 2017.</p><p>"Polya's program for the Riemann Hypothesis and related problems"</p><ul><li><p>Why does Ramanujan, "The man who knew infinity," matter?</p></li><li><p>Polya's program for the Riemann Hypothesis and related problems</p></li><li><p>Can't you just feel the moonshine?</p></li></ul><p><img src="assets/images/2017-Wiener-Ono.jpg" alt="poster" title="" /></p>ARTIN workshop at the University of ManchesterGeorge McNinchgeorge.mcninch@tufts.edu2017-09-15T12:00:00-0400<p>The <a href="https://sites.google.com/view/artin51-manchester/home">Workshop on Lie Theory, Representation Theory and Algebraic
Groups</a> was
held at the University of Manchester (UK) Sept 11-14, 2017.</p><p>I contributed a lecture on <em>Nilpotent orbits of a reductive group over
a local field</em>.</p>Workshop on Pseudo-reductive groups at Newcastle UniversityGeorge McNinchgeorge.mcninch@tufts.edu2017-09-09T12:00:00-0400<p>My colleague <a href="https://www.staff.ncl.ac.uk/david.stewart/">David
Stewart</a> organized a
<a href="https://sites.google.com/view/prgs-newcastle/home">workshop on Pseudo-reductive
groups</a> in
September 2017, which was partially funded by the Heilbronn Institute.</p><p>In this workshop, Gopal Prasad gave a mini-course on his work with
Conrad and Gabber on pseudo-reductive groups.</p><p>I contributed a lecture on <em>Reductive subgroups of parahoric group schemes</em>.
Here is the abstract for my talk:</p><blockquote><p>Let K be the field of fractions of a complete discrete valuation ring
A with residue field k, and let G be a connected reductive algebraic
group over K. Suppose P is a parahoric group scheme attached to G. In
particular, P is a smooth affine A-group scheme having generic fiber
P_K = G; the group scheme P is in general not reductive over A. Assume
that G splits over an unramified extension of K.</p><p>The talk will give an overview of two results about G.</p><p>First, there is a closed and reductive A-subgroup scheme M of P for
which the special fiber M_k is a Levi factor of P_k. Moreover, the
reductive subgroups of G=P_K of the form M_K may be characterized.</p><p>Second, let X be a nilpotent section in Lie(P). We say that X is
balanced if the fibers C_K and C_k are smooth group schemes of the
same dimension, where C=C_P(X) is the scheme theoretic centralizer of
X. If X_0 is a given nilpotent element in the Lie algebra of the
reductive quotient of the special fiber P_k, we give results on the
possible <em>lifts</em> of X_0 to a balanced nilpotent section X of Lie(P).</p></blockquote>Special Session in AMS sectional meeting at Bowdoin CollegeGeorge McNinchgeorge.mcninch@tufts.edu2016-09-26T12:00:00-0400<p>The Fall Eastern AMS sectional meeting was held at Bowdoin College in
Brunswick ME on Sept 24-25, 2016. Tony Iarrobino (Northeastern Univ),
Leila Khatami (Union College) and Julianna Tymoczko (Smith College)
organized a Special Session on <a href="http://www.ams.org/meetings/sectional/2238_program_ss18.html#title">Combinatorial Aspects of Nilpotent
Orbits</a>
at this meeting, and I contributed a talk on <em>Nilpotent elements and
sections</em>.</p><p>Here are the <a href="assets/slides/2016-09---Bowdoin---comparing-centralizers.pdf">slides to my talk</a>.</p>Worshop on local representation theory at the Centre Intrafacultaire BernoulliGeorge McNinchgeorge.mcninch@tufts.edu2016-07-30T12:00:00-0400<p>I was an academic visitor for about 3 weeks in July 2016 at the <a href="http://cib.epfl.ch/">Centre Intrafacultaire
Bernoulli</a>, l'École Polytechnique Fédérale de
Lausanne (EPFL, Switzerland) during the program on <em>Local
Representation Theory and Simple Groups</em> organized by Donna Testerman
(EPFL), Gunter Malle (TU Kaiserslautern), and Radha Kessar (City
University London).</p><p>I enjoyed following lectures by Markus Linckelmann (City University
London), Meinolf Geck (Universität Stuttgart), Marc Cabanes
(Université Paris Diderot), Britta Späth (Bergische Universität
Wuppertal), and Olivier Dudas (Université Paris Diderot) on - among
other things - block theory, and aspects of the
Deligne-Lusztig description of representations of finite reductive
groups.</p>Institut Mittag-Leffler workshop on Branching Problems for Reductive GroupsGeorge McNinchgeorge.mcninch@tufts.edu2016-06-01T08:00:00-0400<p>In May 2016, I attended a week-long workshop on <a href="http://www.mittag-leffler.se/workshop/branching-problems-reductive-groups"><em>Branching Problems
for Reductive
Groups</em></a>
at the <a href="http://www.mittag-leffler.se">Institut Mittag-Leffler</a> (Djursholm, Sweden).</p><p>I gave a lecture on <em>An overview of representations of reductive
algebraic groups</em>; essentially everything I discussed can be found in
the text of Jens Jantzen on the representation theory of algebraic
groups. I tried to focus on things that seemed relevant to the
difficulties presented by modular representation theory to “branching
problems”: (Hochschild) cohomology, the description of simple
representations for reductive groups, reduction mod \(p\) and the
Jantzen filtration of Weyl modules.</p><p>Here are the <a href="assets/slides/2016-05---Mittag-Leffler---reductive-reps--transparencies.pdf">slides from my talk</a>.</p>Noam Elkies delivers Norbert Wiener Lectures at Tufts UniversityGeorge McNinchgeorge.mcninch@tufts.edu2016-04-09T12:00:00-0400<p><a href="http://www.math.harvard.edu/~elkies/">Noam Elkies (Harvard University)</a> gave the <a href="http://math.tufts.edu/seminars/lecturesWiener.htm">Wiener
Lectures in the Tufts University Math
Department</a> in
April 2016.</p><ul><li><p><strong>Canonical forms: the mathematical structure of musical canons</strong> (Public Lecture)</p></li><li><p><strong>Poisson summation and packing problems</strong> (Colloquium talk)</p></li></ul>