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<p>INSTITUTE FOR ADVANCED STUDY<br>
School of Mathematics<br>
Princeton, NJ 08540<br>
<br>
Mathematics Seminars<br>
Week of December 2, 2019</p>
<ul>
<li>On Tuesday, December 3, the lunch time Seminar on Theoretical
Machine Learning <b>is replaced by IAS-PNI Seminar on ML and
Neuroscience presented by Matthew Botvinick</b>
(<a class="moz-txt-link-freetext" href="https://www.math.ias.edu/calendar/event/148504/1575403200/1575408600">https://www.math.ias.edu/calendar/event/148504/1575403200/1575408600</a>)</li>
<ul>
<li>Time and location: <b>3:00-4:30pm, Princeton Neuroscience
Institute, Room A32</b></li>
</ul>
<li>On Thursday, December 5 & Friday December 6 there are <b>Special
Seminars on Hilbert's 13th Problem</b></li>
<ul>
<li>Thursday Seminar Time and location: <b>1:00-1:55pm,
Simonyi Hall 101</b>
(<a class="moz-txt-link-freetext" href="https://www.math.ias.edu/calendar/event/148370/1575568800/1575572100">https://www.math.ias.edu/calendar/event/148370/1575568800/1575572100</a>)</li>
<li>Friday Seminar Time and location: <b>2:00-2:55pm, Simonyi
Hall 101</b>
(<a class="moz-txt-link-freetext" href="https://www.math.ias.edu/calendar/event/148371/1575658800/1575662100">https://www.math.ias.edu/calendar/event/148371/1575658800/1575662100</a>)</li>
</ul>
</ul>
<p><br>
--------------<br>
To view mathematics in titles and abstracts, please click on the
talk's link.<br>
--------------<br>
<br>
Monday, December 2<br>
<br>
Computer Science/Discrete Mathematics Seminar I<br>
Topic: Rainbow fractional matchings<br>
Speaker: Ron Holzman, Technion<br>
Time/Room: 11:00am - 12:00pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=144887">http://www.math.ias.edu/seminars/abstract?event=144887</a><br>
<br>
Members' Seminar<br>
Topic: Mathematical models of human memory<br>
Speaker: Michail Tsodyks, C.V. Starr Professor, School of
Natural Sciences<br>
Time/Room: 2:00pm - 3:00pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=129476">http://www.math.ias.edu/seminars/abstract?event=129476</a><br>
<br>
Symplectic Dynamics/Geometry Seminar<br>
Topic: Disjoint Lagrangian spheres and cyclic dilations<br>
Speaker: Yin Li, King's College London<br>
Time/Room: 3:30pm - 4:30pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145024">http://www.math.ias.edu/seminars/abstract?event=145024</a><br>
<br>
Analysis Seminar<br>
Topic: Distance estimate on Kähler manifolds<br>
Speaker: Yang Li, Member, School of Mathematics<br>
Time/Room: 5:00pm - 6:00pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145363">http://www.math.ias.edu/seminars/abstract?event=145363</a><br>
<br>
<br>
<br>
Tuesday, December 3<br>
<br>
Computer Science/Discrete Mathematics Seminar II<br>
Topic: TBA<br>
Speaker: Fan Wei, Member, School of Mathematics<br>
Time/Room: 10:30am - 12:30pm/Simonyi Hall 101<br>
<br>
IAS-PNI Seminar on ML and Neuroscience<br>
Topic: A distributional code for value in dopamine-based
reinforcement learning<br>
Speaker: Matthew Botvinick, DeepMind<br>
Time/Room: 3:00pm - 4:30pm/Princeton Neuroscience Institute,
Room A32<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148504">http://www.math.ias.edu/seminars/abstract?event=148504</a><br>
<br>
Joint IAS/Princeton University Number Theory Seminar<br>
Topic: Thin groups and the arithmetic of imaginary
quadratic fields<br>
Speaker: Katherine Stange, University of Colorado, Boulder<br>
Time/Room: 4:30pm - 5:30pm/Princeton University, Fine Hall 214<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148412">http://www.math.ias.edu/seminars/abstract?event=148412</a><br>
<br>
<br>
<br>
Wednesday, December 4<br>
<br>
Seminar on Theoretical Machine Learning<br>
Topic: Uncoupled isotonic regression<br>
Speaker: Jonathan Niles-Weed, New York University; Member,
School of Mathematics<br>
Time/Room: 12:00pm - 1:30pm/Dilworth Room<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=132177">http://www.math.ias.edu/seminars/abstract?event=132177</a><br>
<br>
Mathematical Conversations<br>
Topic: TBA<br>
Speaker: Michelangelo Naim, Weizmann Institute of Science;
Visitor, School of Natural Sciences<br>
Time/Room: 6:00pm - 7:00pm/White-Levy<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=147474">http://www.math.ias.edu/seminars/abstract?event=147474</a><br>
<br>
<br>
<br>
Thursday, December 5<br>
<br>
Working Seminar on Nonabelian Hodge Theory<br>
Time/Room: 10:00am - 12:00pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145150">http://www.math.ias.edu/seminars/abstract?event=145150</a><br>
<br>
Special Seminar on Hilbert's 13th Problem I<br>
Topic: The Geometry of Hilbert's 13th problem<br>
Speaker: Jesse Wolfson, University of California, Irvine<br>
Time/Room: 1:00pm - 1:55pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148370">http://www.math.ias.edu/seminars/abstract?event=148370</a><br>
<br>
Working Seminar in Algebraic Number Theory<br>
Time/Room: 2:00pm - 4:00pm<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145219">http://www.math.ias.edu/seminars/abstract?event=145219</a><br>
<br>
Joint IAS/Princeton University Number Theory Seminar<br>
Topic: Higher order uniformity of the Möbius function<br>
Speaker: Joni Teräväinen, University of Oxford<br>
Time/Room: 4:30pm - 5:30pm/Princeton University, Fine 214<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145291">http://www.math.ias.edu/seminars/abstract?event=145291</a><br>
<br>
<br>
<br>
Friday, December 6<br>
<br>
Special Seminar on Hilbert's 13th Problem II<br>
Topic: Topology of resolvent problems<br>
Speaker: Benson Farb, University of Chicago<br>
Time/Room: 2:00pm - 2:55pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148371">http://www.math.ias.edu/seminars/abstract?event=148371</a><br>
<br>
Analysis - Mathematical Physics<br>
Topic: Cardy embedding of random planar maps<br>
Speaker: Nina Holden, ETH Zuerich<br>
Time/Room: 3:30pm - 4:30pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=147451">http://www.math.ias.edu/seminars/abstract?event=147451</a><br>
<br>
Analysis - Mathematical Physics<br>
Topic: TBA<br>
Speaker: Mihalis Dafermos, Princeton University<br>
Time/Room: 5:00pm - 6:00pm/Simonyi Hall 101<br>
Abstract Link:
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=147460">http://www.math.ias.edu/seminars/abstract?event=147460</a><br>
<br>
1 Rainbow fractional matchings<br>
Ron Holzman<br>
<br>
Given a family of m matchings in a graph G (where each matching
can be thought of as a color class), a rainbow matching is a
choice of edges of distinct colors that forms a matching. How many
matchings of size n are needed to guarantee the existence of a
rainbow matching of size n? If G is bipartite, a theorem of Drisko
generalized by Aharoni and Berger says that m = 2n - 1 suffices
(and is best possible). In a general graph G, this is not the
case, but m = 2n is conjectured to be enough. We prove a
fractional version of this conjecture, not only for graphs but
also for r-uniform hypergraphs. The main tool is a topological
result of Kalai and Meshulam. This is joint work with Ron Aharoni
and Zilin Jiang.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=144887">http://www.math.ias.edu/seminars/abstract?event=144887</a><br>
<br>
2 Mathematical models of human memory<br>
Michail Tsodyks<br>
<br>
Human memory is a multi-staged phenomenon of extreme complexity,
which results in highly unpredictable behavior in real-life
situations. Psychologists developed classical paradigms for
studying memory in the lab, which produce easily quantifiable
measures of performance at the cost of using artificial content,
such as lists of randomly assembled words. I will introduce a set
of simple mathematical models describing how information is
maintained and recalled in these experiments. Surprisingly, they
provide a very good description of experimental data obtained with
internet-based memory experiments on large number of human
subjects. Moreover, more detailed mathematical analysis of the
models leads to some interesting ideas for future experiments with
potentially very surprising results.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=129476">http://www.math.ias.edu/seminars/abstract?event=129476</a><br>
<br>
3 Disjoint Lagrangian spheres and cyclic dilations<br>
Yin Li<br>
<br>
An exact Calabi-Yau structure, originally introduced by Keller, is
a special kind of smooth Calabi-Yau structures in the sense of
Kontsevich-Vlassopoulos. For a Weinstein manifold, an exact
Calabi-Yau structure on the wrapped Fukaya category induces a
class in the degree one equivariant symplectic cohomology, which
we call a cyclic dilation. We prove that for many Weinstein
manifolds with cyclic dilations, there is an upper bound on the
number of pairwise disjoint Lagrangian spheres, and the homology
classes of these Lagrangian spheres are non-trivial. On the other
hand, we show that the Milnor fiber of a 3-fold triple point
admits a cyclic dilation despite that there is no quasi-dilation.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145024">http://www.math.ias.edu/seminars/abstract?event=145024</a><br>
<br>
4 Distance estimate on Kähler manifolds<br>
Yang Li<br>
<br>
I will prove the following surprising fact: on a given Kahler
manifold (X, J, \omega), a Holder bound on the Kahler potential
\phi implies a Holder bound on the distance function of the new
Kahler metric \omega+dd^c \phi. Time permitting I will also
discuss the ramifications of this result, and some backgrounds in
pluripotential theory.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145363">http://www.math.ias.edu/seminars/abstract?event=145363</a><br>
<br>
5 A distributional code for value in dopamine-based reinforcement
learning<br>
Matthew Botvinick<br>
<br>
Twenty years ago, a link was discovered between the
neurotransmitter dopamine and the computational framework of
reinforcement learning. Since then, it has become well established
that dopamine release reflects a reward prediction error, a
surprise signal that drives learning of reward predictions and
shapes future behavior. According to the now canonical theory,
reward predictions are represented as a single scalar quantity,
which supports learning about the expectation, or mean, of
stochastic outcomes. I'll present recent work in which we have
proposed a novel account of dopamine-based reinforcement learning,
and adduced experimental results which point to a significant
modification of the standard reward prediction error theory.
Inspired by recent artificial intelligence research on
distributional reinforcement learning, we hypothesized that the
brain represents possible future rewards not as a single mean, but
instead as a probability distribution, effectively representing
multiple future outcomes simultaneously and in parallel. This idea
leads immediately to a set of empirical predictions, which we
tested using single-unit recordings from mouse ventral tegmental
area. Our findings provide strong evidence for a neural
realization of distributional reinforcement learning.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148504">http://www.math.ias.edu/seminars/abstract?event=148504</a><br>
<br>
6 Thin groups and the arithmetic of imaginary quadratic fields<br>
Katherine Stange<br>
<br>
The Farey subdivision of the real line describes the action of
PSL(2,Z) and gives a continued fraction algorithm approximating
real numbers by rational numbers. Asmus Schmidt defined an
analogue for the complex plane, depending on a choice of Euclidean
imaginary quadratic field. I generalize his construction to
arbitrary imaginary quadratic fields, which gives rise to an
arrangement of circles into orbits of the Bianchi group
PSL(2,O_K). Geometric aspects of this picture relate to
arithmetic properties of the field. Furthermore, Apollonian
circle packings arise naturally from the Gaussian case. The
curvatures of integral Apollonian circle packings conjecturally
satisfy a local-global property for which a density-one statement
was proven by Bourgain and Kontorovich. Inspired by the
viewpoint of Schmidt arrangements, we can define an infinite
family of integral circle packings for which the methods of
Bourgain-Kontorovich generalize (joint work with Elena Fuchs and
Xin Zhang). Daniel Martin has recently generalized these pictures
to provide a continued fraction algorithm for non-Euclidean
imaginary quadratic fields.<br>
<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148412">http://www.math.ias.edu/seminars/abstract?event=148412</a><br>
<br>
7 Uncoupled isotonic regression<br>
Jonathan Niles-Weed<br>
<br>
The classical regression problem seeks to estimate a function f on
the basis of independent pairs (x_i,y_i) where ????[y_i]=f(x_i),
i=1,…n. In this talk, we consider statistical and computational
aspects of the "uncoupled" version of this problem, where one
observes only the unordered sets {x_1,…,x_n} and {y_1,…,y_n} and
still hopes to recover information about f. Under the assumption
that f is nondecreasing, we give minimax statistical rates under
weak moment conditions on y_i and provide an efficient algorithm
achieving the optimal rates. Both upper and lower bounds employ
moment-matching arguments based on optimal transport theory. Joint
work with Philippe Rigollet.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=132177">http://www.math.ias.edu/seminars/abstract?event=132177</a><br>
<br>
<br>
<br>
8 The Geometry of Hilbert's 13th problem<br>
Jesse Wolfson<br>
<br>
Given a polynomial in one variable, what is the simplest formula
for the roots in terms of the coefficients? Hilbert conjectured
that for polynomials of degree 6,7 and 8, any formula must involve
functions of at least 2, 3 and 4 variables respectively (such
formulas were first constructed by Hamilton). In a little-known
paper, Hilbert sketched how the 27 lines on a cubic surface should
give a 4-variable solution of the general degree 9 polynomial. In
this talk I’ll recall Klein and Hilbert's geometric reformulation
of solving polynomials, explain the gaps in Hilbert's sketch and
how we can fill these using modern methods. As a result, we obtain
best-to-date upper bounds on the number of variables needed to
solve a general degree n polynomial for all n, improving results
of Segre and Brauer.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148370">http://www.math.ias.edu/seminars/abstract?event=148370</a><br>
<br>
<br>
<br>
9 Higher order uniformity of the Möbius function<br>
Joni Teräväinen<br>
<br>
In a recent work, Matomäki, Radziwill and Tao showed that the
Möbius function is discorrelated with linear exponential phases on
almost all intervals of length $X^{\varepsilon}$. I will discuss
joint work where we generalize this result to nilsequences, so as
a special case the Möbius function is shown not to correlate with
polynomial phases on almost all intervals of length
$X^{\varepsilon}$. As an application, we show that the number of
sign patterns of length $k$ that the Liouville function takes
grows superpolynomially in $k$.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=145291">http://www.math.ias.edu/seminars/abstract?event=145291</a><br>
<br>
10 Topology of resolvent problems<br>
Benson Farb<br>
<br>
In this talk I will describe a topological approach to some
problems about algebraic functions due to Klein and Hilbert. As a
sample application of these methods, I will explain the solution
to the following problem of Felix Klein: Let $\Phi_{g,n}$ be the
algebraic function that assigns to a (principally polarized)
abelian variety its $n$-torsion points. What is the minimal $d$
such that, after a rational change of variables, $\Phi_{g,n}$ can
be written as an algebraic function of $d$ variables? This is
joint work with Mark Kisin and Jesse Wolfson.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=148371">http://www.math.ias.edu/seminars/abstract?event=148371</a><br>
<br>
11 Cardy embedding of random planar maps<br>
Nina Holden<br>
<br>
A random planar map is a canonical model for a discrete random
surface which is studied in probability theory, combinatorics,
mathematical physics, and geometry. Liouville quantum gravity is a
canonical model for a random 2D Riemannian manifold with roots in
the physics literature. In a joint work with Xin Sun, we prove a
strong relationship between these two natural models for random
surfaces. Namely, we prove that the random planar map converges in
the scaling limit to Liouville quantum gravity under a discrete
conformal embedding which we call the Cardy embedding.<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars/abstract?event=147451">http://www.math.ias.edu/seminars/abstract?event=147451</a><br>
<br>
<br>
<br>
IAS Math Seminars Home Page:<br>
<a class="moz-txt-link-freetext" href="http://www.math.ias.edu/seminars">http://www.math.ias.edu/seminars</a><br>
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