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talks.html
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<!DOCTYPE html>
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<title>Tom Mainiero - Talks</title>
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<table class="navigation">
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<td align="center"><h1 class="navname">Tom Mainiero</h1> </td>
<td align="right">
<nav>
<a class="menu" href="index.html"><div class="navit">About</div></a>
<a class="menu" href="research.html"><div class="navit">Research</div></a>
<a class="menu" href="talks.html"><div class="navit-idem">Talks</div></a>
<a class="menu" href="contact.html"><div class="navit">Contact</div></a>
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<p> <b>Disclaimer</b>: Handwritten notes posted here are what I used for the actual talk, but they were never intended to be seen by the public: most contain unreferenced results, and likely contain errors.
These talks can potentially expose you to ideas known to the State of California to cause confusion.
<h1 style="text-align:center">Recorded Talks</h1>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Higher Entropy</div>
<div class="locationdate">
<a href="https://web.archive.org/web/20221115152413/https://www.gc.cuny.edu/events/categorical-semantics-entropy">
Symposium on Categorical Semantics of Entropy ("sycsey")</a>;
CUNY graduate center; May 13, 2022</div>
</p>
<!-- <iframe width="560" height="315" src="https://www.youtube-nocookie.com/watch?v=6cFDviX0hUs" frameborder="0" allow="accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> -->
<p><a href="https://www.youtube.com/watch?v=6cFDviX0hUs">Link to Video on YouTube</a>
<p>Handwritten Notes: <a href="files/scanned_talks/CUNY_SCSEY_051322_HigherEntropy.pdf">PDF</a>
<p><a id="talk-higherentropy-abslink" href="javascript:textExpand('show', 'higherentropy');">Show Abstract</a>
<div id="talk-higherentropy-abs" class="abstract" style="display:none">
Is the frowzy state of your desk no longer as thrilling as it once was?
Are numerical measures of information no longer able to satisfy your needs?
There is a cure!
In this talk we'll learn about: the secret topological lives of multipartite measures and quantum states;
how a homological probe of this geometry reveals correlated random variables;
the sly decategorified involvement of Shannon, Tsallis, Réyni, and von Neumann in this larger geometric conspiracy;
and the story of how Gelfand, Neumark, and Segal's construction of von Neumann algebra representations can help us uncover this informatic ruse.
So come to this talk, spice up your entropic life, and bring new meaning to your relationship with disarray.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">The Secret Topological Life of Shared Information</div>
<div class="locationdate">
<a href="https://indico.cern.ch/event/938492/">
String Math 2020</a>;
July 29, 2020.</div>
</p>
<!-- <iframe width="560" height="315" src="https://www.youtube-nocookie.com/embed/XgbZSwRlAjU" frameborder="0" allow="accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> -->
<p><a href="https://www.youtube.com/watch?v=XgbZSwRlAjU">Link to Video on YouTube</a>
<p>Slides: <a href="files/slides/StringMath_072920_SecretTopologicalLifeofSharedInfo.pdf">Error-Corrected Slides (PDF)</a> or <a href="https://indico.cern.ch/event/938492/contributions/3956387/attachments/2084205/3502189/Mainiero.pdf">Slides Used in Recorded video</a>
<p><a id="talk-secretlife-abslink" href="javascript:textExpand('show', 'secretlife');">Show Abstract</a>
<div id="talk-secretlife-abs" class="abstract" style="display:none">
Sike!
There was no abstract.
This was a post-apocalyptic Zoom talk for the <a href="https://indico.cern.ch/event/938492/">2020 String Math conference</a>.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">The Joy of Watching your BPS States Grow Up.</div>
<div class="locationdate">
<a href="https://physics.tamu.edu/events/the-joy-of-watching-your-bps-states-grow-up/">
Texas A&M High Energy Theory Seminar</a>; September 8, 2014.</div>
</p>
<!-- <iframe width="560" height="315" src="https://www.youtube-nocookie.com/embed/V8wn6hUwHUk" frameborder="0" allow="accelerometer clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> -->
<p><a href="https://www.youtube.com/watch?v=AMxjlM9Wyok">Link to Video on YouTube</a>
<!-- old link using flash: http://mediamatrix.tamu.edu/streams/533188/Tom_Mainiero_Seminar -->
<p>Typed Notes: <a href="files/Texas_AM_Sept2014.pdf">PDF</a> </li>
<p>Handwritten Notes: <a href="files/scanned_talks/TexasAM_HETSeminar_090814_JoyofBPSGrowth.pdf">PDF</a> or <a href="files/scanned_talks/TexasAM_HETSeminar_090814_JoyofBPSGrowth.tar.gz">tar.gz</a> (PNG images)
<p><a id="talk-growup-abslink" href="javascript:textExpand('show', 'growup');">Show Abstract</a>
<div id="talk-growup-abs" class="abstract" style="display:none">
N=2 SU(3) Super-Yang-Mills possesses a rather unexpected property: the number of BPS states of mass less than M grows exponentially with M; moreover, the states contributing to this large growth in the density of states represent bound states that become arbitrarily large in size.
We will discuss the techniques used to derive this result (which may generalize far beyond N=2 SU(3) SYM)—focusing on the machinery of spectral networks—and some possible consequences.
</div>
</div>
<hr class="dashed">
<h1 style="text-align:center">Other External/Invited Talks</h1>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Higher Information: The untold topological secrets of information</div>
<div class="locationdate">
<a href="https://web.archive.org/web/20231125175843/https://www.its.caltech.edu/~vigneaux/igps/">Caltech; Information, Geometry, and Physics Seminar</a>;
Nov. 8, 2023</div>
</p>
<p>Slides: <a href="files/slides/Caltech_110823_HigherInfo.pdf">PDF</a>
<p> <a id="talk-spaceout-abslink" href="javascript:textExpand('show', 'spaceout');">Show Abstract</a>
<div id="talk-spaceout-abs" class="abstract" style="display:none">
In the futuristic year 2023, an ex cohomological cop (Harrison Ford) is pulled out of retirement to track down obstructions to the factorizability of multipartite measures: entangled states and their classical counterparts...joint probability measures.
A vast conspiracy is uncovered: associated to every multipartite measure is an emergent space whose topology encodes non-local correlations between various subsystems.
Probing this space with tools with homology, homotopy, and category theory reveals evidence that entropy and mutual information are Euler characteristics: puppets in a larger informatic ruse.
Join as we slowly uncover pieces of the big picture, unmasking filthy rich measures of shared information higher up on the food chain (complex).
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">A Probability Talk That Spaces Out</div>
<div class="locationdate">
<a href="https://web.archive.org/web/20211010212610/https://math.la.asu.edu/~kotschwar/seminars/dg/spring2018.html">Arizona State University; Differential Geometry and Control Systems Seminar</a>;
Jan. 18, 2018.</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/ASU_DiffGeoSeminar_011818_ProbabilityThatSpacesOut.pdf">PDF</a>
<p> <a id="talk-spaceout-abslink" href="javascript:textExpand('show', 'spaceout');">Show Abstract</a>
<div id="talk-spaceout-abs" class="abstract" style="display:none">
That guy who retired at 25 to Sedona to practice reading auras of upside-down cerebral crystal nudists practicing cannabis yoga might have accidentally said something relevant to physics: space can emerge from the connectedness of things.
I will describe how a topological space emerges from a question about independence of random variables; the topology/geometry encodes information about correlations.
This story is the classical version of a quantum mechanical one, and is inspired by research into the relationship of entangled states and non-trivial geometries of space-time.
Just don't encourage that guy.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">(Dr.) Strangeduality or: how I learned to stop dozing off and learned to love (the) Boolean algebras</div>
<div class="locationdate">
<a href="https://web.archive.org/web/20231125181328/https://math.la.asu.edu/~kotschwar/seminars/dg/fall2016.html">Arizona State University; Differential Geometry and Control Systems Seminar</a>;
Nov. 4, 2016.</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/ASU_DiffGeoSeminar_110416_DrStrangeDuality.pdf">PDF</a> or <a href="files/scanned_talks/ASU_DiffGeoSeminar_110416_DrStrangeDuality.tar.gz">tar.gz</a> (PNG images)
<p> <a id="talk-grandma-abslink" href="javascript:textExpand('show', 'grandma');">Show Abstract</a>
<div id="talk-grandma-abs" class="abstract" style="display:none">
<p> Boolean algebras: your grandma has been hyping them up since the 1930's.
But you're still not convinced that you can afford the quantity coffee that would keep you awake for her logic lectures, in-between her snoring sessions on the couch.
That is, until you hear about Stone duality: every Boolean algebra lives a double life as an oddball topological space.
It doesn't get much attention, but Stone duality is part of the larger theme of the duality between algebras and spaces.
During my talk, I'll channel your grandma to describe Stone duality and, time-permitting, it's relation to measure theory as well as how it relates to other duality theorems.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Morse(t) I listen to this Talk?</div>
<div class="locationdate">
<a href="https://web.archive.org/web/20231125181515/https://math.la.asu.edu/~kotschwar/seminars/dg/fall2015.html">Arizona State University; Differential Geometry and Control Systems Seminar</a>;
Nov. 11, 2015.</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/ASU_DiffGeoSeminar_110615_MorseIListen.pdf">PDF</a> or <a href="files/scanned_talks/ASU_DiffGeoSeminar_110615_MorseIListen.tar.gz">tar.gz</a> (PNG images)
<p> <a id="talk-morse-abslink" href="javascript:textExpand('show', 'morse');">Show Abstract</a>
<div id="talk-morse-abs" class="abstract" style="display:none">
1982: Freddie Mercury is still the lead vocalist for Queen and Ed Witten provides a physical interpretation of the Morse-Smale complex in "Supersymmetry and Morse Theory".
I'll give a colloquium-style overview of this historic paper (from a modern, retrospective viewpoint); outlining how de Rham cohomology of a compact smooth manifold can be extracted from the study of the (supersymmetric) quantum mechanics of a point particle living on that manifold, and how Morse homology arises as a "classical limit" of this theory.
Such ideas formed the basis for the development of Floer homology, among other things.
Familiarity with physics terminology will be useful, but not necessary; similarly an appreciation for synthesizers and reverence of Reagan are not required.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Functional Equations and DT-invariants from Spectral Networks: Revenge of the m-herds</div>
<div class="locationdate">Emphasis Year Workshop on Rep. Theory, Integrable Systems, and Quantum Fields (Northwestern); May 14, 2014.</div>
</p>
<p> Handwritten Notes: <a href="files/scanned_talks/Northwestern_EYWorkshop_051414_RevengeOfTheHerds.pdf">PDF</a> or <a href="files/scanned_talks/Northwestern_EYWorkshop_051414_RevengeOfTheHerds.tar.gz">tar.gz</a> (PNG images)
<p> <a id="talk-funeq-abslink" href="javascript:textExpand('show', 'funeq');">Show Abstract</a>
<div id="talk-funeq-abs" class="abstract" style="display:none">
(Apparently I didn't make an abstract for this talk; feel free to invent your own.)
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Quantum Chern Simons</div>
<div class="locationdate">
<a href="https://web.archive.org/web/20230127075933/https://www.pims.math.ca/scientific-event/140707-wcatss">
West Coast Algebraic Topology Summer School
</a>
(UBC); July 10, 2014.</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/UBC_WCATSS_071014_QuantumCS.pdf">PDF</a> or <a href="files/scanned_talks/UBC_WCATSS_071014_QuantumCS.tar.gz">tar.gz</a> (PNG images)
<p><div id="quantcs" class="abstract">
This was a talk for a summer school; Lecture 1.4 of <a href="https://web.archive.org/web/20221207222356/https://www.pims.math.ca/files/WCATSS_Syllabus-_Full-_Vjune26.pdf">
the description here
</a>.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">This one weird trick has algebraic functions generating Donaldson-Thomas invariants from home! Sit in this talk to see why!</div>
<div class="locationdate">
<a href="https://web.archive.org/save/https://www.math.ksu.edu/research/centers-groups/m-center/past_seminars/2014.html">
Kansas State Mathematics M-seminar</a>;
November 4, 2014</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/Kansas_MSeminar_110414_OneWeirdTrickDT.pdf">PDF</a> or <a href="files/scanned_talks/Kansas_MSeminar_110414_OneWeirdTrickDT.tar.gz">tar.gz</a> (PNG images)
<p><a id="talk-weirdtrick-abslink" href="javascript:textExpand('show', 'weirdtrick');">Show Abstract</a>
<div id="talk-weirdtrick-abs"class="abstract" style="display:none">
It is a result of Kontsevich and Soibelman that generating functions for Donaldson-Thomas (DT) invariants associated to the m-Kronecker quiver are algebraic functions over the rationals. Using a technique from supersymmetric physics-- "spectral networks" -- one can see algebraicity of such functions directly and construct the associated algebraic equations in an algorithmic manner. We will discuss some interesting corollaries of these algebraic equations-- namely asymptotics on DT-invariants and Euler-characteristics of (Kronecker) quiver moduli-- and (if time allows) give a brief overview of the spectral network technique.
</div>
</div>
<hr class="dashed">
<h1 style="text-align:center">Internal (Local) Talks</h1>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Homological Toolkit for the Quantum Mechanic Part III</div>
<div class="locationdate">Rutgers NHETC Subgroup Meeting; February 14, 2019.</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/Rutgers_SubgroupMeet_021419_HomologicalToolkit-iii.pdf">PDF</a>
<p><a id="talk-homtoolkitIII-abslink" href="javascript:textExpand('show', 'homtoolkitIII');">Show Abstract</a>
<div id="talk-homtoolkitIII-abs" class="abstract" style="display:none">
This talk abides by the Hollywood rule: it's not dead until you see the body.
We will recap the main ideas of the previous talks (so don't worry if you haven't seen them or cannot remember much).
We'll introduce presheaves of vector spaces from the data of a multipartite state and show how the associated Cech cochain complexes are the complexes predicted from previous talks.
The cohomology of such complexes outputs tuples of operators that exhibit non-local correlations caused by entanglement.
If there is time we will make brief mention about the classical analogues of this construction, where the cohomology is the cohomology of an actual space.
Why waste time seeking tinder hookups on Valentine's day when you can \hookrightarrow yourself into the NHETC common room?
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Homological Toolkit for the Quantum Mechanic Part II</div>
<div class="locationdate">Rutgers NHETC Subgroup Meeting; October 11, 2018.</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/Rutgers_SubgroupMeet_092718_HomologicalToolkit-ii.pdf">PDF</a>
<p><a id="talk-homtoolkitII-abslink" href="javascript:textExpand('show', 'homtoolkitII');">Show Abstract</a>
<div id="talk-homtoolkitII-abs" class="abstract" style="display:none">
This is the second talk in a three part talk series.
See the abstract for Part I below.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Homological Toolkit for the Quantum Mechanic Part I</div>
<div class="locationdate">Rutgers NHETC Subgroup Meeting; September 27, 2018.</div>
</p>
<p>Handwritten Notes: To Appear (Available on Request)
<p><a id="talk-homtoolkitI-abslink" href="javascript:textExpand('show', 'homtoolkitI');">Show Abstract</a>
<div id="talk-homtoolkitI-abs" class="abstract" style="display:none">
This is the first part of an N-part series about entanglement and homological algebra; here N is large and equal to 2 or 3.
After a short overview, we will encounter the mutual information of a multipartite density state as measure of "entanglement" (more precisely: lack of factorizability).
It leads a secret life as the limit of a triholomorphic index that is invariant under local unitary (or invertible) transformations and plays nicely with tensor products and "classical sums".
What else is it hiding?
Is its trihomolorphic persona the Euler characteristic of something?
Find out next week in another episode of States of our Lives.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Big Machinery in Quantum Mechanics: An Intro to Cohomology as a Tool for Quantifying Multipartite Entanglement.</div>
<div class="locationdate">Rutgers NHETC Subgroup Meeting; October 13, 2017.</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/Rutgers_SubgroupMeet_101317_BigMachinery.pdf">PDF</a> or <a href="files/scanned_talks/Rutgers_SubgroupMeet_101317_BigMachinery.tar.gz">tar.gz</a> (PNG images)
<p><a id="talk-bigmachine-abslink" href="javascript:textExpand('show', 'bigmachine');">Show Abstract</a>
<div id="talk-bigmachine-abs" class="abstract" style="display:none">
In the futuristic year 2017 Piscataway, NJ is a depressing metropolis filled with urban decay. An ex-Cohomological cop (Harrison Ford) is pulled out of retirement to track down obstructions to the calculation of expectation values in terms of local quantities, caused by the presence of entangled states that came to the planet Earth in search of non-local correlations. With the help of C*-algebra representation theory of Gelfand, Naimark, and Segal, he closes in on a chain complex outputting obstructions to factorizability in the form of tuples of multi-body non-locally correlated operators---but his hatred for numerical valued quantities is called into question when he realizes the Euler characteristic is related to (q-deformations of) multivariate mutual information.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Entanglement is a Global Conspiracy Encoded in a Graded Vector Space</div>
<div class="locationdate">Rutgers NHETC Group Meeting; March 17, 2016</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/Rutgers_GroupMeet_031716_GlobalConspiracy.pdf">PDF</a> or <a href="files/scanned_talks/Rutgers_GroupMeet_031716_GlobalConspiracy.tar.gz">tar.gz</a> (PNG images)
<p><a id="talk-conspiracy-abslink" href="javascript:textExpand('show', 'conspiracy');">Show Abstract</a>
<div id="talk-conspiracy-abs" class="abstract" style="display:none">
Nowadays the idea of entanglement being related to non-trivial geometries or topologies is about as surprising as a solitary carrot.
Typically global/topologically non-trivial data can be extracted from a (co)homology theory.
I will describe some ideas and partial results relating to why (multipartite) entanglement may be encoded in a homology theory and the dream of extracting entanglement entropy (more accurately: mutual information) as the Euler characteristic of a chain complex.
This talk will be just linear algebra, not an attempt to put you to sleep with a jargon lullaby.
</div>
</div>
<hr class="dashed">
<div class= "textbox">
<p>
<div class = "talktitle">Fourier-Mukai: A perspective from the village idiot</div>
<div class="locationdate">Student Seminar on Geometric Langlands (UT Austin); February 17, 2015</div>
</p>
<p>Handwritten Notes: <a href="files/scanned_talks/UT_LanglandsSeminar_021715_FourierMukai.pdf">PDF</a> or <a href="files/scanned_talks/UT_LanglandsSeminar_021715_FourierMukai.tar.gz">tar.gz</a> (PNG images)
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I will attempt to convey a superficial understanding of the Fourier-Mukai transform (in particular for abelian varieties).
This is the third talk in a series on GL_1 Geometric Langlands.
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<div class = "talktitle">What is a Formal Derived Stack?</div>
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<a href="https://web.archive.org/web/20231125165104/https://web.ma.utexas.edu/users/rhughes/DAGX/DAG.html">
Derived Algebraic Geometry Seminar
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(UT Austin); March 25, 2015.</div>
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<p>Handwritten Notes: <a href="files/scanned_talks/UT_DAGXSeminar_032515_FormalDerivedStacks.pdf">PDF</a> or <a href="files/scanned_talks/UT_DAGXSeminar_032515_FormalDerivedStacks.tar.gz">tar.gz</a> (PNG images)
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This was a talk for a seminar on Derived Algebraic Geometry co-organized by <a href="https://www.richardderryberry.com/">Richard Derryberry</a> and Aaron Royer.
Details and references can be found <a href="https://web.archive.org/web/20240224131152/https://web.ma.utexas.edu/users/rhughes/DAGX/DAG.html">here</a>.
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<div class = "talktitle">Get Stoked about Stokes Groupoids</div>
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<a href="https://web.archive.org/web/20231125194518/https://golem.ph.utexas.edu/wiki/gst/show/Spring+2014">
Geometry and String Theory Seminar (UT Austin)</a>;
April 23, 2014</div>
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<p>Handwritten Notes: <a href="files/scanned_talks/UT_GST_042314_GetStokedAboutStokesGroupoids.pdf">PDF</a>
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The Riemann-Hilbert correspondence is a statement about a correspondence between the study of flat connections on bundles over a manifold X, and representations of its fundamental group(oid).
In the case that X is a complex curve, however, many folks take pleasure in the study of the fancier world of flat connections with singularities bounded by some divisor D < X.
Gualtieri, Li, and Pym (1305.7288) state that in this world, the appropriate Riemann-Hilbert correspondence tells us that the study of such flat connections is the study of representations of a groupoid \Pi(X,D).
Despite all of the "oiding," the results are quite simple and reveal a beautiful (and "functorial") way to take formal power series solutions (of flat sections) to honest solutions by looking at pull-backs to the groupoid \Pi(X,D).
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<div class = "talktitle">Clifford Algebras and Dirac Operators</div>
<div class="locationdate"><a href="https://web.archive.org/web/20231125165018/https://web.ma.utexas.edu/users/rhughes/ASIT/ASIT.html">Atiyah Singer Index Theorem Student Seminar</a> (UT Austin); June 13, 2013</div>
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<p>Handwritten Notes: <a href="files/scanned_talks/UT_ASIT_061313_CliffordAlgebrasDiracOps.pdf">PDF</a>
<p>Attendee Notes (Richard Derryberry): <a href="https://web.archive.org/web/20231125165321/https://web.ma.utexas.edu/users/rhughes/ASIT/ASIT03Clifford_algebras_and_Dirac_operators_%28Tom_Mainiero%29.pdf">PDF</a>
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This was a talk given as part of a student-run seminar on the Atiyah-Singer Index Theorem, organized by <a href="https://www.richardderryberry.com/">Richard Derryberry</a>.
A link to the seminar series, which includes various notes taken by Richard is <a href="https://web.ma.utexas.edu/users/rhughes/ASIT/ASIT.html">here</a>.
In case of bit-rot, an internet archive link is <a href="https://web.archive.org/web/20231125165018/https://web.ma.utexas.edu/users/rhughes/ASIT/ASIT.html">here</a>.
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<div class = "talktitle">Understanding Theory X via Discrete Light Cone Quantization</div>
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<a href="https://golem.ph.utexas.edu/wiki/gst/revision/HomePage/98">Geometry and String Theory Seminar (UT Austin)</a>;
November 11, 2013.</div>
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<p>Handwritten Notes: <a href="files/scanned_talks/UT_GST_111313_TheoryXviaDLCQ.pdf">PDF</a>
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The year is 1997.
N M5 branes have collided and the fate of the world(volume theory) rests on understanding Theory X: the 6D (2,0) theory.
In this talk we'll sketch the ideas behind discrete light cone quantization (DLCQ), Matrix models for M-theory (the BFSS conjecture) , and the subsequent application of DLCQ to Theory X (of type A_{N-1}).
You won't even need to hang up your rotary phone to access the internet.
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<div class = "talktitle"> Bethe Subalgebras, counting, and integrability</div>
<div class="locationdate">Geometry and String Theory Seminar (UT Austin); March 20, 2013.</div>
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<p>Handwritten Notes: <a href="files/scanned_talks/UT_GST_032013_BetheSubalgebras.pdf">PDF</a> or <a href="files/scanned_talks/UT_GST_032013_BetheSubalgebras.tar.gz">tar.gz</a> (PNG images)
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We will continue Pavel's discussion from last time, fitting the XXX spin chain into a larger set of models with a Yangian-module structure.
Integrability will follow by introducing a commutative subalgebra of the Yangian and outsourcing the Hamiltonian counting problem to a local elementary school.
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