Difference between revisions of "WVU Math Colloquia"

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'''Wednesdays at 4pm EDT'''<br />
+
'''Mondays at 4pm EDT'''<br /> Armstrong Hall 315
−
[https://wvu.zoom.us/j/96317244165?pwd=YVJGWHdxb2lGUHlkZEdRT1NPRFFsUT09 zoom link] (pass ''mathAdi2'')
+
[https://wvu.zoom.us/j/91064873237?pwd=R2lMSkpDUHREaU1xeUdDeVJHT2ZaUT09 zoom link] (pass ''euclid2022'')
  
  
 +
The 2022-2023 WVU Math Colloquium is organized by Chris Ciesielski, Robert Mnatsakanov and Casian Pantea.
 +
Talks are usually held on Mondays at 4pm in Armstrong Hall 315 (in some cases we will schedule the seminar at different days/times, to accommodate speakers).
  
−
The 2021-2022 Applied Mathematics Seminar is organized by Adrian Tudorascu and Casian Pantea.
+
If you'd like to suggest speakers for the fall semester please contact Chris, Robert, or Casian.
−
The talks are on zoom until further notice. The regular time for the Seminar is on Wednesday at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).
 
  
−
If you'd like to suggest speakers for the fall semester please contact Adrian or Casian.
 
  
  
−
 
+
= Schedule =
−
= Analysis Seminar Schedule =
 
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!align="left" | date   
 
!align="left" | date   
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|align="left" | '''institution'''
 
|align="left" | '''institution'''
 
!align="left" | title
 
!align="left" | title
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!align="left" | host(s)
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!align="left" | notes
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|-
 
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|September 21, VV B139
 
−
| Dóminique Kemp
 
−
| UW-Madison
 
−
|[[#Dóminique Kemp  |  Decoupling by way of approximation ]]
 
−
|
 
−
|-
 
−
|September 28, VV B139
 
−
| Jack Burkart
 
−
| UW-Madison
 
−
|[[#Jack Burkart  |  Transcendental Julia Sets with Fractional Packing Dimension ]]
 
−
|
 
−
|-
 
−
|October 5, Online
 
−
| Giuseppe Negro
 
−
| University of Birmingham
 
−
|[[#Giuseppe Negro  |  Stability of sharp Fourier restriction to spheres ]]
 
−
|
 
−
|-
 
−
|October 12, VV B139
 
−
|Rajula Srivastava
 
−
|UW Madison
 
−
|[[#Rajula Srivastava  |  Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups ]]
 
−
|
 
−
|-
 
−
|October 19, Online
 
−
|Itamar Oliveira
 
−
|Cornell University
 
−
|[[#Itamar Oliveira  |  A new approach to the Fourier extension problem for the paraboloid ]]
 
−
|
 
−
|-
 
−
|October 26, VV B139
 
−
| Changkeun Oh
 
−
| UW Madison
 
−
|[[#Changkeun Oh  |  Decoupling inequalities for quadratic forms and beyond ]]
 
−
|
 
−
|-
 
−
|October 29, Colloquium
 
−
| Alexandru Ionescu
 
−
| Princeton University
 
−
|[[#Alexandru Ionescu  |  Polynomial averages and pointwise ergodic theorems on nilpotent groups]]
 
−
|-
 
−
|November 2, VV B139
 
−
| Liding Yao
 
−
| UW Madison
 
−
|[[#Liding Yao  |  An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains ]]
 
−
|
 
−
|-
 
−
|November 9, VV B139
 
−
| Lingxiao Zhang
 
−
| UW Madison
 
−
|[[#Lingxiao Zhang  |  Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition ]]
 
−
|
 
−
|-
 
−
|November 12, Colloquium
 
−
| Kasso Okoudjou
 
−
| Tufts University
 
−
|[[#Kasso Okoudjou  |  An exploration in analysis on fractals ]]
 
−
|-
 
−
|November 16, VV B139
 
−
| Rahul Parhi
 
−
| UW Madison (EE)
 
−
|[[#Rahul Parhi  |    On BV Spaces, Splines, and Neural Networks ]]
 
−
|
 
−
|-
 
−
|November 30, VV B139
 
−
| Alexei Poltoratski
 
−
| UW Madison
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|December 7
 
−
| TBA
 
−
| TBA
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|December 14
 
−
| Tao Mei
 
−
| Baylor University
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|February 1
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
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|
 
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|-
 
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|February 8
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
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|
 
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|-
 
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|February 15
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
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|
 
−
|-
 
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|February 22
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
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|
 
−
|-
 
−
|March 1
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|March 8
 
−
| Brian Street
 
−
| UW Madison
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|March 15: No Seminar
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|March 23
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
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|
 
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|-
 
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|March 30
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|April 5
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
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|
 
−
|-
 
−
|April 12
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|April 19
 
−
| Person
 
−
| Institution
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|April 22, Colloquium
 
−
|Detlef Müller
 
−
|University of Kiel
 
−
|[[#linktoabstract  |  Title ]]
 
−
|
 
−
|-
 
−
|April 25, 4:00 p.m., Distinguished Lecture Series
 
−
|Larry Guth
 
−
|MIT
 
−
|[[#linktoabstract  |  Title ]]
 
 
|-
 
|-
−
|April 26, 4:00 p.m., Distinguished Lecture Series
+
|September 15
−
|Larry Guth
+
| Dehua Wang
−
|MIT
+
| University of Pittsburgh
−
|[[#linktoabstract |  Title ]]
+
|[[#Dehua Wang |  Elastic effects on vortex sheets and vanishing viscosity ]]
 +
| 2:30pm, 315 ARM
 +
|
 
|-
 
|-
−
|April 27, 4:00 p.m., Distinguished Lecture Series
+
|October 17
−
|Larry Guth
+
| Farhad Jafari
−
|MIT
+
| University of Minnesota
−
|[[#linktoabstract  |   Title ]]
+
|[[#Farhad Jafari | Variational Problems, Moment Sequences and Positive Definiteness ]]
−
|  
+
|
 
|-
 
|-
−
|May 3
+
|October 24
−
| Person
+
| Tóth János
−
| Institution
+
| Budapest University of Technology and Economics
−
|[[#linktoabstract |   Title ]]
+
|[[#Tóth János | The concept of reaction extent ]]
−
|  
+
|
 
|-
 
|-
−
|Date
+
|October 31
−
| Person
+
| Zi-Xia Song
−
| Institution
+
| University of Central Florida
−
|[[#linktoabstract |   Title ]]
+
|[[#Zi-Xia Song | Coloring Graphs with Forbidden Minors ]]
−
|  
+
|
 
|-
 
|-
 +
|November 14
 +
| Benjamin Bagozzi
 +
| University of Delaware
 +
|[[#Benjamin Bagozzi | Understanding the Politics of Information Access in Big Data Contexts ]]
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
−
===Dóminique Kemp===
 
−
 
−
Decoupling by way of approximation
 
−
 
−
Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.
 
−
 
−
===Jack Burkart===
 
−
 
−
Transcendental Julia Sets with Fractional Packing Dimension
 
−
 
−
If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.
 
−
 
−
In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.
 
−
 
−
===Giuseppe Negro===
 
−
 
−
Stability of sharp Fourier restriction to spheres
 
−
 
−
In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate.
 
−
 
−
Joint work with E.Carneiro and D.Oliveira e Silva.
 
−
 
−
===Rajula Srivastava===
 
−
 
−
Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups
 
−
 
−
We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.
 
−
 
−
===Itamar Oliveira===
 
−
 
−
A new approach to the Fourier extension problem for the paraboloid
 
−
 
−
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $  of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.
 
−
 
−
===Changkeun Oh===
 
−
 
−
Decoupling inequalities for quadratic forms and beyond
 
−
 
−
In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.
 
−
 
−
===Alexandru Ionescu===
 
−
 
−
Polynomial averages and pointwise ergodic theorems on nilpotent groups
 
−
 
−
I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.
 
−
 
−
===Liding Yao===
 
−
 
−
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains
 
−
 
−
Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.
 
  
−
===Lingxiao Zhang===
+
===Dehua Wang===
  
−
Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition
+
'''''Elastic effects on vortex sheets and vanishing viscosity'''''
  
−
We study operators of the form
+
Elasticity is important in continuum mechanics with a wide
−
$Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$
+
range of applications and is challenging in analysis. In this talk we
−
where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.
+
shall first review some basic mathematical results and then discuss
 +
some special elastic effects in fluid flows. The first elastic effect
 +
is the stabilizing effect of elasticity on the vortex sheets in
 +
compressible elastic flows. Some recent results on linear and
 +
nonlinear stability of compressible vortex sheets will be presented.
 +
The second effect is on the vanishing viscosity process of
 +
compressible viscoelastic flows in the half plane under the no-slip
 +
boundary condition. Our results show that the deformation tensor can
 +
prevent the formation of strong boundary layers. The talk is based on
 +
the recent joint works with several collaborators.
  
−
===Kasso Okoudjou===
+
===Farhad Jafari===
  
−
An exploration in analysis on fractals
+
'''''Variational  Problems, Moment Sequences and Positive Definiteness'''''
  
−
Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.
+
Our ability to reformulate many problems in science and engineering in terms of variational  (and control) problems continue to keep this area of mathematics current and of great interest. In this presentation we reformulate these problems as problems in measure theory and use moment methods to study them. Relating variational problems to moment methods has brought new interest in moment methods, moment completion problems and algebras of rational functions. This talk will connect these areas and (briefly) will show applications of moment methods to reconstruction problems in tomography.
  
−
===Rahul Parhi===
+
===Tóth János===
  
−
On BV Spaces, Splines, and Neural Networks
+
'''''The concept of reaction extent'''''
  
−
Many problems in science and engineering can be phrased as the problem
+
The concept of reaction extent or the progress of a reaction, advancement of the reaction, conversion, etc. was introduced around 100 years ago.
−
of reconstructing a function from a finite number of possibly noisy
+
Most of the literature provides a definition for the exceptional case of a single reaction step or gives an implicit definition that cannot be made explicit.  
−
measurements. The reconstruction problem is inherently ill-posed when
+
Starting from the standard definition we extend the classic definition of the reaction extent in explicit form for an arbitrary number of species
−
the allowable functions belong to an infinite set. Classical techniques
+
and of reaction steps and arbitrary kinetics. Then, we study the mathematical properties (evolution equation, continuity, monotony, differentiability, etc.) of the defined quantity, and connect them to the formalism of modern reaction kinetics.
−
to solve this problem assume, a priori, that the underlying function has
+
Our approach tries to adhere to the customs of chemists and be mathematically correct simultaneously.
−
some kind of regularity, typically Sobolev, Besov, or BV regularity. The
 
−
field of applied harmonic analysis is interested in studying efficient
 
−
decompositions and representations for functions with certain
 
−
regularity. Common representation systems are based on splines and
 
−
wavelets. These are well understood mathematically and have been
 
−
successfully applied in a variety of signal processing and statistical
 
−
tasks. Neural networks are another type of representation system that is
 
−
useful in practice, but poorly understood mathematically.
 
  
−
In this talk, I will discuss my research which aims to rectify this
+
We also show how to apply this concept to exotic reactions: reactions with more than one stationary state, oscillatory reactions, and reactions showing chaotic behavior. With the new definition, one can calculate not only the time evolution of the concentration of each reacting species but also the number of occurrences of the individual reaction events.
−
issue by understanding the regularity properties of neural networks in a
 
−
similar vein to classical methods based on splines and wavelets. In
 
−
particular, we will show that neural networks are optimal solutions to
 
−
variational problems over BV-type function spaces defined via the Radon
 
−
transform. These spaces are non-reflexive Banach spaces, generally
 
−
distinct from classical spaces studied in analysis. However, in the
 
−
univariate setting, neural networks reduce to splines and these function
 
−
spaces reduce to classical univariate BV spaces. If time permits, I will
 
−
also discuss approximation properties of these spaces, showing that they
 
−
are, in some sense, "small" compared to classical multivariate spaces
 
−
such as Sobolev or Besov spaces.
 
  
−
This is joint work with Robert Nowak.
+
This is joint work with Vilmos Gáspár.
  
−
=[[Previous_Analysis_seminars]]=
+
=== Zi-Xia Song===
  
−
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars
+
'''''Coloring Graphs with Forbidden Minors'''''
  
−
=Extras=
+
[[Media:SongAbstract.png|'''Abstract link''']]
  
−
[[Blank Analysis Seminar Template]]
 
  
 +
===Benjamin Bagozzi===
  
−
Graduate Student Seminar:
+
'''''Understanding the Politics of Information Access in Big Data Contexts'''''
  
−
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
+
Access to information (ATI) systems empower groups and individuals to request information from their governments and obligate these governments to respond, subject to certain legal exemptions. These systems are now in operation in over 100 countries worldwide. The data that are generated by ATI systems can often be characterized as having (i) fine-grained spatio-temporal properties, (ii) extensive amounts of text, (iii) sender-receiver characteristics, and (iv) potential privacy concerns. For political science, such data offer researchers an opportunity to study questions related to government responsiveness, bureaucratic performance, and public accountability at near-unprecedented levels of disaggregation. This presentation highlights the opportunities and challenges associated with ATI data for both data science and political science audiences. Its focus is primarily on Mexico's federal ATI system and over two million associated ATI requests and responses covering the 2003-2020 period. Applications of supervised and unsupervised machine learning tools to the texts of these requests and their responses will be presented, alongside analyses of these request-response measures in relation to government responsiveness in Mexico.

Latest revision as of 19:12, 26 October 2022

Mondays at 4pm EDT
Armstrong Hall 315 zoom link (pass euclid2022)


The 2022-2023 WVU Math Colloquium is organized by Chris Ciesielski, Robert Mnatsakanov and Casian Pantea. Talks are usually held on Mondays at 4pm in Armstrong Hall 315 (in some cases we will schedule the seminar at different days/times, to accommodate speakers).

If you'd like to suggest speakers for the fall semester please contact Chris, Robert, or Casian.


Schedule

date speaker institution title notes
September 15 Dehua Wang University of Pittsburgh Elastic effects on vortex sheets and vanishing viscosity 2:30pm, 315 ARM
October 17 Farhad Jafari University of Minnesota Variational Problems, Moment Sequences and Positive Definiteness
October 24 Tóth János Budapest University of Technology and Economics The concept of reaction extent
October 31 Zi-Xia Song University of Central Florida Coloring Graphs with Forbidden Minors
November 14 Benjamin Bagozzi University of Delaware Understanding the Politics of Information Access in Big Data Contexts

Abstracts

Dehua Wang

Elastic effects on vortex sheets and vanishing viscosity

Elasticity is important in continuum mechanics with a wide range of applications and is challenging in analysis. In this talk we shall first review some basic mathematical results and then discuss some special elastic effects in fluid flows. The first elastic effect is the stabilizing effect of elasticity on the vortex sheets in compressible elastic flows. Some recent results on linear and nonlinear stability of compressible vortex sheets will be presented. The second effect is on the vanishing viscosity process of compressible viscoelastic flows in the half plane under the no-slip boundary condition. Our results show that the deformation tensor can prevent the formation of strong boundary layers. The talk is based on the recent joint works with several collaborators.

Farhad Jafari

Variational Problems, Moment Sequences and Positive Definiteness

Our ability to reformulate many problems in science and engineering in terms of variational (and control) problems continue to keep this area of mathematics current and of great interest. In this presentation we reformulate these problems as problems in measure theory and use moment methods to study them. Relating variational problems to moment methods has brought new interest in moment methods, moment completion problems and algebras of rational functions. This talk will connect these areas and (briefly) will show applications of moment methods to reconstruction problems in tomography.

Tóth János

The concept of reaction extent

The concept of reaction extent or the progress of a reaction, advancement of the reaction, conversion, etc. was introduced around 100 years ago. Most of the literature provides a definition for the exceptional case of a single reaction step or gives an implicit definition that cannot be made explicit. Starting from the standard definition we extend the classic definition of the reaction extent in explicit form for an arbitrary number of species and of reaction steps and arbitrary kinetics. Then, we study the mathematical properties (evolution equation, continuity, monotony, differentiability, etc.) of the defined quantity, and connect them to the formalism of modern reaction kinetics. Our approach tries to adhere to the customs of chemists and be mathematically correct simultaneously.

We also show how to apply this concept to exotic reactions: reactions with more than one stationary state, oscillatory reactions, and reactions showing chaotic behavior. With the new definition, one can calculate not only the time evolution of the concentration of each reacting species but also the number of occurrences of the individual reaction events.

This is joint work with Vilmos Gáspár.

Zi-Xia Song

Coloring Graphs with Forbidden Minors

Abstract link


Benjamin Bagozzi

Understanding the Politics of Information Access in Big Data Contexts

Access to information (ATI) systems empower groups and individuals to request information from their governments and obligate these governments to respond, subject to certain legal exemptions. These systems are now in operation in over 100 countries worldwide. The data that are generated by ATI systems can often be characterized as having (i) fine-grained spatio-temporal properties, (ii) extensive amounts of text, (iii) sender-receiver characteristics, and (iv) potential privacy concerns. For political science, such data offer researchers an opportunity to study questions related to government responsiveness, bureaucratic performance, and public accountability at near-unprecedented levels of disaggregation. This presentation highlights the opportunities and challenges associated with ATI data for both data science and political science audiences. Its focus is primarily on Mexico's federal ATI system and over two million associated ATI requests and responses covering the 2003-2020 period. Applications of supervised and unsupervised machine learning tools to the texts of these requests and their responses will be presented, alongside analyses of these request-response measures in relation to government responsiveness in Mexico.

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