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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML>
<HEAD>
<TITLE>Workshop on Polynomial Functors</TITLE>
<LINK REL="stylesheet" HREF="pfunk.css" TYPE="text/css">
</HEAD>
<BODY>
<script language="JavaScript" type="text/JavaScript">
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<TABLE CLASS="frontpagetable" CELLSPACING="0" WIDTH="100%">
<TR>
<TD>
<IMG ALIGN="left" width="330" SRC="frame-zoom.jpg" ALT="Photo">
</TD>
<TD WIDTH="400">
<H1>2022 Workshop on Polynomial Functors</H1>
At the <A HREF="http://topos.institute">Topos Institute</A> and
online via Zoom<BR>
2022 March 14–18 (UTC)
</TD>
</TR>
</TABLE>
<HR>
<P>
Participants will learn background material and hear the latest progress on polynomial functors. The main topic is the notion of polynomial functors in locally cartesian closed (LCC) categories, as employed in logic and type theory (the theme of last year's workshop). However we also include a tutorial and talks on the notion of polynomial functors in the sense of Eilenberg and Mac Lane, hoping to uncover connections between these two notions.
<P>
This is the second workshop in a series. The <A
HREF="2021">first Workshop on
Polynomial Functors</A> was held in March 2021.
<br><br>
<a href="https://topos-institute.zoom.us/j/82168450200?pwd=SGZEV2U1cnBBU1JNY0dYNFFCbWd5dz09">Zoom link</a>
<H3>Speakers</H3>
<TABLE class="speakerstable">
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://www.andrew.cmu.edu/user/awodey/">Steve Awodey x2</A>:</TD>
<TD class="topic">
<div id="awodeylog" style="DISPLAY: block">
<a href="javascript:swaptabs('awodeyexp','awodeylog');">
► <EM>Tutorial: Polynomial functors and type theory</EM> </a> </div>
<div id="awodeyexp" style="DISPLAY: none">
<a href="javascript:swaptabs('awodeylog','awodeyexp');">
▼ <EM>Tutorial: Polynomial functors and type theory</EM> </a>
<br>
| <a href="./slides/Awodey1.pdf">Awodey slides, day 1</a><br>
| <a href="./slides/Awodey2.pdf">Awodey slides, day 2</a>
<br>Abstract: This 2-lecture tutorial will explain the connection between dependent type theory and polynomial functors first explored in [1].
The first lecture presents the basic notion of a "natural model" of type theory, a functorial reformulation of the concept of a "category with families", capturing the syntax of dependent type theory. We show how the usual type theoretic rules of dependent sums and products correspond to the structure of a polynomial monad on the associated natural model, and an algebra for that monad. In part 2 we show what it means to add identity types and universes to the type theory, consider the relation between natural models and Joyal's "tribes", and state some open problems.
<br>
<br>
[1] S. Awodey, Natural models of homotopy type theory, Mathematical Structures in Computer Science 28(2), pp. 241–286 (2018)
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://science.ucalgary.ca/mathematics-statistics/contacts/kristine-bauer">Kristine Bauer</A>:</TD>
<TD class="topic">
<div id="bauerlog" style="DISPLAY: block">
<a href="javascript:swaptabs('bauerexp','bauerlog');">
► <EM>Categorical differentiation and Goodwillie polynomial functors</EM> </a> </div>
<div id="bauerexp" style="DISPLAY: none">
<a href="javascript:swaptabs('bauerlog','bauerexp');">
▼ <EM>Categorical differentiation and Goodwillie polynomial functors</EM> </a>
<br>
| <a href="./slides/Bauer">Bauer's slides</a>
<br>Abstract: The Eilenberg-Maclane notion of polynomial functors was used by Goodwillie to construct a tower of approximations of a homotopy functor similar to the way in which the Taylor Series provides approximations to functions of real variables. In this talk, I will explain the construction of the functor calculus tower and address the analogy with the Taylor Series by explaining how the derivative of a functor in the sense of Goodwillie is a categorical derivative.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://math.unice.fr/~cberger/">Clemens Berger</A>:</TD>
<TD class="topic">
<div id="bergerlog" style="DISPLAY: block">
<a href="javascript:swaptabs('bergerexp','bergerlog');">
► <EM>Goodwillie's cubical cross-effects and nilpotency in semiabelian categories</EM> </a> </div>
<div id="bergerexp" style="DISPLAY: none">
<a href="javascript:swaptabs('bergerlog','bergerexp');">
▼ <EM>Goodwillie's cubical cross-effects and nilpotency in semiabelian categories</EM> </a>
<br>
| <a href="./slides/Berger.pdf">Berger's slides</a>
<br>Abstract:
In the original approach of Eilenberg-MacLane, polynomial
functors are characterised by the vanishing of certain recursively
defined cross-effects. Later on, Goodwillie uses cubical combinatorics
to give a one-step definition of these cross-effects, opening thus the
possibility to define polynomial functors in a non-additive setting.
In this talk, I will explain how Goodwillie's cubical cross-effects
lead quite naturally to an intrinsic understanding of nilpotent
objects in semiabelian categories. This is based on joint work with
Dominique Bourn.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://www.irif.fr/~curien/">Pierre-Louis Curien</A>:</TD>
<TD class="topic">
<div id="curienlog" style="DISPLAY: block">
<a href="javascript:swaptabs('curienexp','curienlog');">
► <EM>Opetopes, opetopic sets and polygraphs</EM> </a> </div>
<div id="curienexp" style="DISPLAY: none">
<a href="javascript:swaptabs('curienlog','curienexp');">
▼ <EM>Opetopes, opetopic sets and polygraphs</EM> </a>
<br>
| <a href="./slides/Curien.pdf">Curien's slides</a>
<br>Abstract: Opetopes are algebraic tree-like descriptions of shapes corresponding to compositions and coherences in higher dimensions. They were introduced by Baez and Dolan. They were later recast in the language of polynomial functors by Kock, Joyal, Batanin, and Mascari, and subsequently in a type-theoretic language by Curien, Ho Thanh and Mimram. On the other hand, polygraphs (also known as computads) are presentations of strict n- or omega-categories all the strict finite truncations of which are free in all dimensions. We will introduce both opetopes and polygraphs, and present a new, elementary, proof of the isomorphism between many-to-one polygraphs on one hand, and opetopic sets (i.e. presheaves on the category of opetopes) on the other hand. This result had been proved quite indirectly by Harnik, Makkai, and Zawadowski in 2008. A more direct proof was given by Ho Tanh in his PhD thesis (2019), with a reference to some results of Simon Henry. The new proof is entirely self-contained, and, more importantly, unveils invariants of the polygraphic syntax.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://eldenelmanto.com">Elden Elmanto</A>:</TD>
<TD class="topic">
<div id="elmantolog" style="DISPLAY: block">
<a href="javascript:swaptabs('elmantoexp','elmantolog');">
► <EM>Bispans in algebraic geometry</EM> </a> </div>
<div id="elmantoexp" style="DISPLAY: none">
<a href="javascript:swaptabs('elmantolog','elmantoexp');">
▼ <EM>Bispans in algebraic geometry</EM> </a>
<br>
| <a href="./slides/Elmanto.pdf">Elmanto's notes or slides</a>
<br>Abstract:
The category of bispans (a.k.a. polynomial diagrams)
is to the category of commutative rings, as the category of spans is to the category of abelian groups. If one believes this, then it is not a stretch that various forms and ideas of algebraic geometry arise from and interact with the category of bispans. I will survey recent work around this idea. Original results presented are with Rune Haugseng, but other results include those of Bachmann-Hoyois and Barwick-Glasman-Mathew-Nikolaus.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://www.cl.cam.ac.uk/~ds709/">Eric Finster</A>:</TD>
<TD class="topic">
<div id="finsterlog" style="DISPLAY: block">
<a href="javascript:swaptabs('finsterexp','finsterlog');">
► <EM>Polynomial Monads and Opetopic Types in Type Theory</EM> </a> </div>
<div id="finsterexp" style="DISPLAY: none">
<a href="javascript:swaptabs('finsterlog','finsterexp');">
▼ <EM>Polynomial Monads and Opetopic Types in Type Theory</EM> </a>
<br>
| <a href="./slides/Finster.pdf">Finster's notes or slides</a>
<br>Abstract:
I will describe how to add a definition of opetopic type to
Martin-Löf type theory by rendering definitional the signature of
certain polynomial monads. Moreover, I will survey some constructions
which can be made in this theory and remark on the outlook for
formalizing higher dimensional structures using this approach.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://www.cl.cam.ac.uk/~mpf23/">Marcelo Fiore</A>:</TD>
<TD class="topic">
<div id="fiorelog" style="DISPLAY: block">
<a href="javascript:swaptabs('fioreexp','fiorelog');">
► <EM>Polynomial modelling of abstract syntax</EM> </a> </div>
<div id="fioreexp" style="DISPLAY: none">
<a href="javascript:swaptabs('fiorelog','fioreexp');">
▼ <EM>Polynomial modelling of abstract syntax</EM> </a>
<br>
| <a href="./slides/Fiore.pdf">Fiore's slides</a>
<br>
Abstract:
The abstract syntax of a formal language is the essential syntactical structure reflecting the semantic import of the language phrases. Abstract syntax has both synthetic and analytic aspects: the former concerns the constructors needed to form phrases, the latter the destructors needed to take them apart. The categorical algebraic point of view regards abstract syntax as an initial algebra: the structure map is synthetic syntax, its inverse is analytic syntax. Initiality provides compositional semantics (as the unique homomorphism to a model) by structural recursion, with an associated principle of structural induction.
<br><br>
Specifications of language phrases are typically given syntactically by means of signatures or, more generally, typing rules. In this talk, I will explain my thesis: (i) that these are notation for polynomial diagrams, and (ii) that abstract syntax arises from the associated polynomial endofunctors by free constructions. I will do so by considering a variety of language features of increasing complexity: mono and multi sorted algebraic term structure, simple and polymorphic type structure (with variable-binding and parametrised-metavariable term structure), and cartesian and/or linear context structure. The mathematical development naturally leads to the consideration of two kinds of polynomial functors: the traditional one between slice categories, arising from locally cartesian closed structure, and another one between presheaf categories, arising from essential geometric morphisms. The former polynomial functors (and their initial algebras) have a type-theoretic rendering as indexed containers (and general trees) that is directly implementable in dependently-typed proof assistants. This is not so for the latter polynomial functors and I will present an approach to bridging this gap via adjoint modalities.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="http://www1.maths.leeds.ac.uk/~pmtng/">Nicola Gambino</A>:</TD>
<TD class="topic">
<div id="gambinolog" style="DISPLAY: block">
<a href="javascript:swaptabs('gambinoexp','gambinolog');">
► <EM>The matrix product of coloured symmetric sequences</EM> </a> </div>
<div id="gambinoexp" style="DISPLAY: none">
<a href="javascript:swaptabs('gambinolog','gambinoexp');">
▼ <EM>The matrix product of coloured symmetric sequences</EM> </a>
<br>
| <a href="./slides/Gambino.pdf">Gambino's notes</a>
<br>Abstract: In 2008, Maia and Méndez defined the operation of
arithmetic product of species of structures, extending the calculus of
species of structures introduced by Joyal. In 2014, Dwyer and Hess
rediscovered independently this operation in the context of symmetric
sequences (as part of their work on Boardman-Vogt tensor product of bimodules)
and named it matrix multiplication.
<br><br>
In this talk, based on joint work in progress with Richard Garner and
Christina Vasilakopoulou, we extend the matrix multiplication from symmetric
sequences to coloured symmetric sequences and show that it determines an
oplax monoidal structure on the the bicategory of coloured symmetric sequences.
In order to do this, we establish general results on lifting monoidal
structures to Kleisli double categories. This approach allows us to
attack and solve the difficult problem of verifying the coherence conditions
for a monoidal bicategory in an efficient way.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://www.union.edu/mathematics/faculty-staff/brenda-johnson">Brenda Johnson</A>:</TD>
<TD class="topic">
<div id="johnsonlog" style="DISPLAY: block">
<a href="javascript:swaptabs('johnsonexp','johnsonlog');">
► <EM>From polynomial functors to functor calculi</EM> </a> </div>
<div id="johnsonexp" style="DISPLAY: none">
<a href="javascript:swaptabs('johnsonlog','johnsonexp');">
▼ <EM>From polynomial functors to functor calculi</EM> </a>
<br>
| <a href="./slides/Johnson.pdf">Johnson's slides</a>
<br>Abstract: The calculus of homotopy functors, developed by Tom Goodwillie,
provides a means of constructing a Taylor-series-like tower of functors for a
suitably nice functor of topological spaces. Use of this "Taylor tower" has led to
significant results in homotopy theory and K-theory. Inspired by Goodwillie's
construction, Kristine Bauer, Randy McCarthy and I developed an analogous functor
calculus, the discrete calculus, based on the polynomial functors of Eilenberg and Mac Lane. In this talk, I will provide an introduction to these functor calculi, and discuss recent work with Kathryn Hess that sets up a general framework for constructing functor calculi.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://users.ox.ac.uk/~univ4449/">Sean Moss</A>:</TD>
<TD class="topic">
<div id="mosslog" style="DISPLAY: block">
<a href="javascript:swaptabs('mossexp','mosslog');">
► <EM>Dependent products of polynomials</EM> </a> </div>
<div id="mossexp" style="DISPLAY: none">
<a href="javascript:swaptabs('mosslog','mossexp');">
▼ <EM>Dependent products of polynomials</EM> </a>
<br>
| <a href="./slides/Moss.pdf">Moss's slides</a>
<br>Abstract:
The category of polynomial functors is cartesian closed but
not locally cartesian closed. Nevertheless, Tamara von Glehn has shown
that it hosts an interesting model of dependent type theory. I'll
discuss this and some variations in relation to Dialectica categories.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://fredriknf.com/">Fredrik Nordvall Forsberg</A>:</TD>
<TD class="topic">
<div id="nordvalllog" style="DISPLAY: block">
<a href="javascript:swaptabs('nordvallexp','nordvalllog');">
► <EM>On the differential structure of polynomial functors</EM> </a> </div>
<div id="nordvallexp" style="DISPLAY: none">
<a href="javascript:swaptabs('nordvalllog','nordvallexp');">
▼ <EM>On the differential structure of polynomial functors</EM> </a>
<br>
| <a href="./slides/NordvallF.pdf">Nordvall Forsberg's notes</a>
<BR>Abstract:
About twenty years ago, McBride noticed a curious connection between
rules for computing the type of 'one-hole contexts' for algebraic data
types, and Leibniz's calculus differentiation rules: they are exactly
the same! Representing algebraic data types by polynomial functors, I
will explain how this is the case, and show that this notion of
derivative of polynomial functors gives rise to a Cartesian
differential category in the sense of Blute, Cockett and Seely.<br><br>
This is joint work with Conor McBride and Neil Ghani.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="">Exequiel Rivas</A>:</TD>
<TD class="topic">
<div id="rivaslog" style="DISPLAY: block">
<a href="javascript:swaptabs('rivasexp','rivaslog');">
► <EM>Procontainers: a proposal from computational effects</EM> </a> </div>
<div id="rivasexp" style="DISPLAY: none">
<a href="javascript:swaptabs('rivaslog','rivasexp');">
▼ <EM>Procontainers: a proposal from computational effects</EM> </a>
<br>
| <a href="./slides/Rivas.pdf">Rivas's slides</a>
<br>Abstract:
Computational effects such as monads (Moggi 1989) and idioms (McBride &
Paterson 2008) are interpreted by functors in the semantics of
programming languages, which in many interesting cases fall under the
sphere of containers (or polynomial functors).
Arrows (Hughes 2000) are a third connected class of computational
effects, but their interpretation is in terms of profunctors rather than
functors, which are outside the scope of (polynomial) functors.
In this talk, we will explore a proposal for a notion of "procontainer"
for capturing a class of profunctors that allows us to reflect some
results from the theory of computational effects relating monads, idioms
and arrows.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://math.cornell.edu/brandon-shapiro">Brandon Shapiro</A>:</TD>
<TD class="topic">
<div id="shapirolog" style="DISPLAY: block">
<a href="javascript:swaptabs('shapiroexp','shapirolog');">
► <EM>Familial Monads for Higher and Lower Category Theory</EM> </a> </div>
<div id="shapiroexp" style="DISPLAY: none">
<a href="javascript:swaptabs('shapirolog','shapiroexp');">
▼ <EM>Familial Monads for Higher and Lower Category Theory
</EM> </a>
<br>
| <a href="./slides/Shapiro.pdf">Shapiro's slides</a>
<br>Abstract:
Familial monads, which are cartesian monads on presheaf categories whose endofunctors are parametric right adjoint (pra), provide a formalism for a class of algebraic structures that includes categories, n-categories, double categories, multicategories, bicategories, and many more algebraic higher category structures. As pra functors arise as bicomodules among polynomial functors (of the bundle variety), this suggests higher category theory has a place in the growing polynomial ecosystem. A drawback of familial monads is that they cannot model algebraic theories with strict commutativity conditions such as commutative monoids, so in this talk I'll show how they can model weak commutativity as in symmetric monoidal categories. Moreover, this construction provides a roadmap for how to encode even strict commutativity conditions in the language of polynomials.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="http://dspivak.net/">David Spivak</A>:</TD>
<TD class="topic">
<div id="spivaklog" style="DISPLAY: block">
<a href="javascript:swaptabs('spivakexp','spivaklog');">
► <EM>Functorial aggregation</EM> </a> </div>
<div id="spivakexp" style="DISPLAY: none">
<a href="javascript:swaptabs('spivaklog','spivakexp');">
▼ <EM>Functorial aggregation</EM> </a>
<br>
| <a href="./slides/Spivak.pdf">Spivak's slides</a>
<br>
Abstract: In this talk I'll explain how various universal operations in the (LCC) polynomial ecosystem combine to solve an applied problem: database aggregation. In particular, we will see that the category of comonoids and bicomodules in Poly has a coclosure operation as well as a local monoidal closed structure. Using these, we'll see how the seemingly atomic operation of <i>transposing a span</i>, or <i>taking the opposite of a category</i>, is actually a composite of two more primitive universal operations: a local dual and an adjoint. The ability of the polynomial ecosystem to so articulately carve nature at its joints seems to be necessary for defining the deceptively simple idea of database aggregation, which can be roughly understood as "integrating along compact fibers".
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://www.paultaylor.eu">Paul Taylor</A>:</TD>
<TD class="topic">
<div id="taylorlog" style="DISPLAY: block">
<a href="javascript:swaptabs('taylorexp','taylorlog');">
► <EM>The Berry Order (Ideas from 1980s stable domain theory)</EM> </a> </div>
<div id="taylorexp" style="DISPLAY: none">
<a href="javascript:swaptabs('taylorlog','taylorexp');">
▼ <EM>The Berry Order (Ideas from 1980s stable domain theory)</EM> </a>
<br>
| <a href="./slides/Taylor.pdf">Taylor's slides</a>
<br>Abstract:
Besides Joyal's "species", the influences on work akin to
polynomial functors in the 1980s were Diers' "multiadjoints",
Berry's initial investigations of "sequential programs"
and Girard's adaptation of this to the semantics of "System F".
<BR><br>
Using Berry's term "stable domain theory", Lamarche and I
constructed numerous cartesian closed (bi)categories of
categories and pullback-preserving functors, looking for
better models of polymorphism.
<BR><br>
In these, the order between maps is not pointwise but the
"Berry order"; for categories the naturality squares must
be pullbacks, so these were called "cartesian transformations".
<BR><br>
The function-spaces turn out to have a simpler representation
than in "Scott" domain theory. This uses what Berry and
Girard called the "trace", which consists of the multiple
universal (unit) maps from Diers' theory, which I called
"candidates".
<BR><br>
The one theorem that I shall prove is that the trace
provides a factorisation system for stable functors.
The "epis" are functors with (single) left adjoints and
the "monos" are those which are equivalences on slices.
The latter are essentially fibrations whose fibres are
groupoids.
<BR><br>
The different "flavours" of stable domains are measured by
the properties of their slices (including familiar notions
from categorical logic for no obvious reason) and the
complexity of the "multicolimits" - both their cardinality
and the kinds of groups that are involved.
<BR><br>
A lot of this material was not written up properly, so
there there is a goldmine waiting for younger researchers
to develop. For example, Gabriel-Ulmer duality between
LFP and lex categories can be extended to "disjunctive"
theories. Also, the similarity between (bi)categories
of domains and the domains themselves that was used to
model System F might be adapted to finding models of
univalence in HoTT.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://topologicalmusings.wordpress.com">Todd Trimble</A>:</TD>
<TD class="topic">
<div id="trimblelog" style="DISPLAY: block">
<a href="javascript:swaptabs('trimbleexp','trimblelog');">
► <EM>Notions of functor for Poly</EM> </a> </div>
<div id="trimbleexp" style="DISPLAY: none">
<a href="javascript:swaptabs('trimblelog','trimbleexp');">
▼ <EM>Notions of functor for Poly</EM> </a>
<br>
| <a href="./slides/Trimble.pdf">Trimble's slides</a>
<br>Abstract:
Fundamental concepts in category theory tend to be expressible in terms of other basic concepts. Categories, for instance, can be seen as monads in spans, or as polynomial comonads, or as simplicial sets satisfying Segal conditions, and so on. The notion of functor similarly enjoys this sort of kaleidoscopic display. In this talk, we will consider functors from various points of view and tailor them to Poly. The tools we use, such as monadicity theorems and allied results, are rather basic, and we hope accessible to a wide audience.
</div>
</TD>
</TR>
<TR>
<TD class="time" style="width: 240">●
<A HREF="https://irma.math.unistra.fr/~vespa/">Christine Vespa x3</A>:</TD>
<TD class="topic">
<div id="vespalog" style="DISPLAY: block">
<a href="javascript:swaptabs('vespaexp','vespalog');">
► <EM>Tutorial: Eilenberg-Mac Lane polynomial functors</EM> </a> </div>
<div id="vespaexp" style="DISPLAY: none">
<a href="javascript:swaptabs('vespalog','vespaexp');">
▼ <EM>Tutorial: Eilenberg-Mac Lane polynomial functors</EM> </a>
<br>
| <a href="./slides/Vespa1.pdf">Vespa notes, day 1</a><br>
| <a href="./slides/Vespa2.pdf">Vespa notes, day 2</a><br>
| <a href="./slides/Vespa3.pdf">Vespa notes, day 3</a>
<br>Abstract: This 3-lecture tutorial is an introduction to the notion of polynomial functors, introduced by Eilenberg and Mac Lane in 1954 as a generalization of additive functors. This notion applies directly to functors from a monoidal category, in which the unit is a zero object, to an abelian category. In these lectures, I will introduce equivalent definitions of polynomial functors and give several examples. After that, I will present some structure results and an overview of applications and other developments.
</div>
</TD>
</TR>
</TABLE>
<H3>Organizers</H3>
<A HREF="http://mat.uab.cat/~kock/">Joachim Kock</A> and
<A HREF="http://dspivak.net">David Spivak</A>
<BR>
<H3>Participation</H3>
<P>
Anyone interested in participating is welcome; an <a href="https://docs.google.com/forms/d/e/1FAIpQLSc5oT7hD2l78ktp5w65gpvJLHU13rH95qdYONx_s_wBVtug8Q/viewform?usp=sf_link">online registration form</a>
is now available.
A zoom link will be sent out to registered participants
a few hours before the workshop.
</P>
For other questions, please contact <A
HREF="mailto:[email protected]">David Spivak</A> or <A
HREF="mailto:[email protected]">Joachim Kock</A>.
<H3>Program</H3>
Each talk will consist of a 50-minute presentation, followed by 10 minutes for questions and coffee break.
Presentations will
take place March 14–18 in the following 4-hour window:
<p>
14:00–18:00 UTC.
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<P>
Japan 23:00–03:00 (+1);
Central Europe 15:00–19:00;
UK 14:00–18:00;
US East Coast 10:00–14:00;
US West Coast 07:00–11:00.
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<br><br>
The following links go directly to the YouTube presentations of the speaker name listed:
<P>
<P>
<TABLE CLASS="timetable" CELLSPACING="0">
<TR>
<TH style="width: 110">Time (UTC)
</TH>
<TH style="width: 140">Monday, 3/14
</TH>
<TH style="width: 140">Tuesday, 15
</TH>
<TH style="width: 140">Wednesday, 16
</TH>
<TH style="width: 140">Thursday, 17
</TH>
<TH style="width: 140">Friday, 18
</TH>
</TR>
<TR>
<TD>14:00–15:00
</TD>
<TD><a href="https://youtu.be/aTZyHHAwk2E?t=222">Awodey 1</a>
</TD>
<TD><a href="https://youtu.be/adnOorfpmEE?t=5">Awodey 2</a>
</TD>
<TD><a href="https://youtu.be/u8XCiI-ZSHc?t=10">Shapiro</a>
</TD>
<TD><a href="https://youtu.be/tw08TmO0RRo?t=8">Berger</a>
</TD>
<TD><a href="https://youtu.be/bzBbOV2pCGE?t=19">Elmanto</a>
</TD>
</TR>
<TR>
<TD>15:00–16:00
</TD>
<TD><a href="https://youtu.be/aTZyHHAwk2E?t=3624">Vespa 1</a>
</TD>
<TD><a href="https://youtu.be/adnOorfpmEE?t=3569">Vespa 2</a>
</TD>
<TD><a href="https://youtu.be/u8XCiI-ZSHc?t=3597">Vespa 3</a>
</TD>
<TD><a href="https://youtu.be/tw08TmO0RRo?t=3626">Bauer</a>
</TD>
<TD><a href="https://youtu.be/bzBbOV2pCGE?t=3562">Spivak</a>
</TD>
</TR>
<TR>
<TD>16:00–17:00
</TD>
<TD><a href="https://youtu.be/aTZyHHAwk2E?t=7364">Trimble</a>
</TD>
<TD><a href="https://youtu.be/adnOorfpmEE?t=7196">Gambino</a>
</TD>
<TD><a href="https://youtu.be/u8XCiI-ZSHc?t=7228">Fiore</a>
</TD>
<TD><a href="https://youtu.be/tw08TmO0RRo?t=7190">Moss</a>
</TD>
<TD><a href="https://youtu.be/bzBbOV2pCGE?t=7164">Rivas</a>
</TD>
</TR>
<TR>
<TD>17:00–18:00
</TD>
<TD><a href="https://youtu.be/aTZyHHAwk2E?t=10958">Nordvall F.</a>
</TD>
<TD><a href="https://youtu.be/adnOorfpmEE?t=10809">Johnson</a>
</TD>
<TD><a href="https://youtu.be/u8XCiI-ZSHc?t=10863">Finster</a>
</TD>
<TD><a href="https://youtu.be/tw08TmO0RRo?t=10819">Taylor</a>
</TD>
<TD><a href="https://youtu.be/bzBbOV2pCGE?t=10809">Curien</a>
</TD>
</TR>
</TABLE>
<HR>
<SMALL>
Last update: 2022-03-18.
</SMALL>
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