[iasmath-semru] Mathematics Seminars -- Week of October 2, 2017
Anthony Pulido
apulido at ias.edu
Fri Sep 29 18:00:17 EDT 2017
INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of October 2, 2017
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To view mathematics in titles and abstracts, please click on the talk's link.
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Monday, October 2
Computer Science/Discrete Mathematics Seminar I
Topic: Crossing the logarithmic barrier for dynamic boolean data structure lower bounds
Speaker: Omri Weinstein, Columbia University
Time/Room: 11:00am - 12:15pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=128772
Seminar on Theoretical Machine Learning
Topic: Hyperparameter optimization: a spectral approach
Speaker: Elad Hazan, Princeton University
Time/Room: 12:30pm - 1:45pm/White-Levy Room
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=133015
Members' Seminar
no seminar: postdoctoral talks
Speaker: no seminar: postdoctoral talks
Time/Room: -
Short talks by postdoctoral members
Topic: Weights of mod $p$ automorphic forms
Speaker: Bao V. Le Hung, Member, School of Mathematics
Time/Room: 2:00pm - 2:15pm/S-101
Topic: Multivariate trace inequalities
Speaker: Marius Lemm, Member, School of Mathematics
Time/Room: 2:15pm - 2:30pm/S-101
Topic: $A_\infty$ structures as a language for open Gromov-Witten theory
Speaker: Sara Tukachinsky, Member, School of Mathematics
Time/Room: 2:30pm - 2:45pm/S-101
Topic: $p$-adic L-functions and Iwasawa main conjectures
Speaker: Zheng Liu, Member, School of Mathematics
Time/Room: 4:00pm - 4:15pm/S-101
Topic: Zeroes of Laplace eigenfunctions and propagation of smallness
Speaker: Aleksandr Logunov, Member, School of Mathematics
Time/Room: 4:15pm - 4:30pm/S-101
Topic: The distribution of primes and zeros of Riemann's Zeta function
Speaker: James Maynard, Member, School of Mathematics
Time/Room: 4:30pm - 4:45pm/S-101
Tuesday, October 3
Computer Science/Discrete Mathematics Seminar II
Topic: Elementary open problems in Algebra (with consequences in computational complexity)
Speaker: Avi Wigderson, Herbert H. Maass Professor, School of Mathematics
Time/Room: 10:30am - 12:30pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=129001
Locally Symmetric Spaces Seminar
Topic: Motivic correlators and locally symmetric spaces
Speaker: Alexander Goncharov, Yale University; Member, School of Mathematics and Natural Sciences
Time/Room: 1:30pm - 4:00pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=132702
Wednesday, October 4
Short talks by postdoctoral members
Topic: On weak epsilon nets and the Radon number
Speaker: Shay Moran, Member, School of Mathematics
Time/Room: 2:00pm - 2:15pm/S-101
Topic: From representations of the symmetric group to branched covers of the disk
Speaker: Amitai Netser Zernik, Member, School of Mathematics
Time/Room: 2:15pm - 2:30pm/S-101
Topic: To Be Announced
Speaker: Behnam Neyshabur, Member, School of Mathematics
Time/Room: 2:30pm - 2:45pm/S-101
Topic: Twisted integral orbit parametrizations
Speaker: Aaron Pollack, Member, School of Mathematics
Time/Room: 4:00pm - 4:15pm/S-101
Topic: Algebraic groups in positive characteristic
Speaker: Srimathy Srinivasan, Member, School of Mathematics
Time/Room: 4:15pm - 4:30pm/S-101
Topic: Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds
Speaker: Michael Lipnowski, Member, School of Mathematics
Time/Room: 4:30pm - 4:45pm/S-101
Thursday, October 5
Working Group on Algebraic Number Theory
Speaker: To Be Announced
Time/Room: 2:00pm - 4:00pm/Jadwin 111, Princeton University
Joint IAS/Princeton University Number Theory Seminar
Topic: Unlikely intersections for algebraic curves in positive characteristic
Speaker: David Masser, University of Basel
Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=131079
Friday, October 6
Short talks by postdoctoral members
Topic: The local multiplicity problem for the Ginzburg-Rallis model and the generalized Shalika model
Speaker: Chen Wan, Member, School of Mathematics
Time/Room: 11:00am - 11:15am/S-101
Topic: Formulas related to Zastava spaces
Speaker: Jonathan Wang, Member, School of Mathematics
Time/Room: 11:15am - 11:30am/S-101
Topic: Finer virtual structure for moduli spaces of holomorphic curves
Speaker: Dingyu Yang, Member, School of Mathematics
Time/Room: 11:30am - 11:45am/S-101
Topic: Geometry of Shimura varieties
Speaker: Rong Zhou, Member, School of Mathematics
Time/Room: 2:00pm - 2:15pm/S-101
Topic: The relative trace formula approach to the global Gan-Gross-Prasad conjecture for unitary groups
Speaker: Michal Zydor, Member, School of Mathematics
Time/Room: 2:15pm - 2:30pm/S-101
Topic: The geometry and topology of minimal surfaces in $\mathbb R^3$ of finite total curvature
Speaker: Otis Chodosh, Member, School of Mathematics
Time/Room: 2:30pm - 2:45pm/S-101
Mathematical Conversations
Topic: To Be Announced
Speaker: Akshay Venkatesh, Stanford University; Distinguished Visiting Professor, School of Mathematics
Time/Room: 6:00pm - 7:00pm/Dilworth Room
Saturday, October 7
Workshop on Topology: Identifying Order in Complex Systems
Topic: Discrete conformal geometry of polyhedral surfaces and its applications
Speaker: Feng Luo, Rutgers University
Time/Room: 9:00am - 10:00am/David Rittenhouse Laboratory A4, University of Pennsylvania
Workshop on Topology: Identifying Order in Complex Systems
Topic: On Morse index estimates for minimal surfaces
Speaker: Davi Maximo, University of Pennsylvania
Time/Room: 10:30am - 11:30am/David Rittenhouse Laboratory A4, University of Pennsylvania
Workshop on Topology: Identifying Order in Complex Systems
Topic: Fast predictive models for image registration
Speaker: Marc Niethammer, University of North Carolina, Chapel Hill
Time/Room: 1:30pm - 2:30pm/David Rittenhouse Laboratory A4, University of Pennsylvania
Workshop on Topology: Identifying Order in Complex Systems
Topic: Personalized cancer therapy using molecular landscape topology and thermodynamics
Speaker: Edward Rietman, University of Massachusetts, Amherst
Time/Room: 3:00pm - 4:00pm/David Rittenhouse Laboratory A4, University of Pennsylvania
Workshop on Topology: Identifying Order in Complex Systems
Topic: Consistent manifold representation for topological data analysis
Speaker: Tim Sauer, George Mason University
Time/Room: 4:30pm - 5:30pm/David Rittenhouse Laboratory A4, University of Pennsylvania
1 Crossing the logarithmic barrier for dynamic boolean data structure
lower bounds
Omri Weinstein
This paper proves the first super-logarithmic lower bounds on the
cell-probe complexity of dynamic boolean (a.k.a. decision) data
structure problems, a long-standing milestone in data structure lower
bounds.
We introduce a new method for proving dynamic cell probe lower bounds
and use it to prove a $\tilde{\Omega}(\log^{1.5} n)$ lower bound on the
operational time of a wide range of boolean data structure problems,
most notably, on the query time of dynamic range counting over
$\mathbb{F}_2$ ([Pat07]). Proving an $\omega(\lg n)$ lower bound for
this problem was explicitly posed as one of five important open problems
in the late Mihai Patrascu's obituary. This result also implies the
first $\omega(\lg n)$ lower bound for the classical 2D range counting
problem, one of the most fundamental data structure problems in
computational geometry and spatial databases. We derive similar lower
bounds for boolean versions of dynamic polynomial evaluation and 2D
rectangle stabbing, and for the (non-boolean) problems of range
selection and range median.
Our technical centerpiece is a new way of ``weakly" simulating dynamic
data structures using efficient one-way communication protocols with
small advantage over random guessing. This simulation involves a
surprising excursion to low-degree (Chebyshev) polynomials which may be
of independent interest, and offers an entirely new algorithmic angle on
the ``cell sampling" method.
Joint work with Kasper Green Larsen and Huacheng Yu.
http://www.math.ias.edu/seminars/abstract?event=128772
2 Hyperparameter optimization: a spectral approach
Elad Hazan
Modern machine learning algorithms often involve complicated models with
tunable parameters, called hyperparameters, that are set during
training. Hyperparameter tuning/optimization is considered an art. (See
e.g. http://www.argmin.net/2016/06/20/hypertuning/ )
We give a simple, fast algorithm for hyperparameter optimization
inspired by techniques from the analysis of Boolean functions. We focus
on the high-dimensional regime where the canonical example is training a
neural network with a large number of hyperparameters. The algorithm -
an iterative application of compressed sensing techniques for orthogonal
polynomials - requires only uniform sampling of the hyperparameters and
is thus easily parallelizable. Experiments for training deep nets on
Cifar-10 show that compared to state-of-the-art tools (e.g., Hyperband
and Spearmint), our algorithm finds significantly improved solutions.
Additionally, our method comes with provable guarantees and yields a
quasi-polynomial time algorithm for learning decision trees under the
uniform distribution with the best known sample complexity.
The talk covers this paper paper: https://arxiv.org/abs/1706.00764 as
well as work in progress.
http://www.math.ias.edu/seminars/abstract?event=133015
3 Elementary open problems in Algebra (with consequences in
computational complexity)
Avi Wigderson
I will survey some elementary (to state!) problems on groups, matrices,
and tensors, and discuss their motivations arising from several major
problems in computational complexity theory. On each problem there was
some exciting recent progress which may raise hope it can be resolved.
No special background will be assumed.
http://www.math.ias.edu/seminars/abstract?event=129001
4 Motivic correlators and locally symmetric spaces
Alexander Goncharov
According to Langlands, pure motives are related to a certain class of
automorphic representations.
Can one see mixed motives in the automorphic set-up? For examples, can
one see periods of mixed motives in entirely automorphic terms? The goal
of this and the next lecture is to supply some examples.
We define motivic correlators describing the structure of the motivic
fundamental group $\pi_1^{\mathcal M}(X)$ of a curve. Their relevance to
the questions raised above is explained by the following examples.
1. Motivic correlators have an explicit Hodge realization given by the
Hodge correlator integrals, providing a new description of the real
mixed Hodge structure of the pro-nilpotent completion of $\pi_1(X)$.
When $X$ is a modular curve, the simplest of them coincide with the
Rankin-Selberg integrals, and the rest provide an "automorphic"
description of a class of periods of mixed motives related to (products
of) modular forms.
2. We use motivic correlators to relate the structure of
$\pi_1^{\mathcal M}(\mathbb G_m − \mu N )$ to the geometry of the
locally symmetric spaces for the congruence subgroup $\Gamma_1 (m; N )
\subset \mathrm{GL}_m(\mathbb Z)$. Then we use the geometry of the
latter, for $m \leq 4$, to understand the structure of the former.
3. This mysterious relation admits an "explanation" for $m = 2$: we
define a canonical map \[ \mu : \text{modular complex} \to \text{the
weight two motivic complex of the modular curve.} \]
Here the complex on the left calculates the singular homology of the
modular curve via modular symbols. The map $\mu$ generalizes the
Belinson-Kato Euler system in $K_2$ of the modular curves.
Composing the map μ with the specialization to a cusp, we recover the
correspondence above at $m = 2$.
4. Yet specializing to CM points on modular curves, we get a new
instance of the above correspondence, now between $\pi_1^{\mathcal M}(E
− E[\mathcal N])$ and geometry of arithmetic hyperbolic threefolds. Here
$E$ is a CM elliptic curve, and $\mathcal N \subset \mathrm{Aut}(E)$ is
an ideal.
http://www.math.ias.edu/seminars/abstract?event=132702
5 Unlikely intersections for algebraic curves in positive characteristic
David Masser
In the last two decades there has been much study of what happens when
an algebraic curve in \(n\)-space is intersected with two multiplicative
relations
\[x_1^{a_1} \cdots x_n^{a_n} = x_1^{b_1} \cdots x_n^{b_n} = 1
\tag{\(\times\)}\]
for \((a_1, \ldots ,a_n),(b_1,\ldots, b_n)\) linearly independent in
\({\bf Z}^n\). Usually the intersection with the union of all
\((\times)\) is at most finite, at least in zero characteristic. This
often becomes false in positive characteristic, and I gave in 2014 a
substitute conjecture and proved it for \(n = 3\). I will describe all
this together with more recent work with Dale Brownawell where we do the
same for additive relations \((+)\); now an extra Frobenius structure
has to be added, and there are no longer any direct analogues in zero
characteristic.
http://www.math.ias.edu/seminars/abstract?event=131079
IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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