Igor Pak Home Page
I am a Professor at the Mathematics Department
at UCLA. I am a member of the
one of the oldest Combinatorics group in the US
(see the History of Combinatorics at UCLA).
Before coming here, I was at
University of Minnesota and
Prior to that, I was a Gibbs Instructor at Yale University
and a Postdoctoral Fellow at MSRI.
I got my Ph.D. from Harvard University.
I did my undergraduate studies at Moscow
State University. I went to Moscow High School 57.
I work in Discrete Mathematics. More specifically, my research spans
the following topics:
My undergraduate advisor was
Kirillov (currently at
UPenn). My graduate advisor was
Persi Diaconis (currently at
Stanford). As a postdoc at Yale,
I was working with
(currently at Eötvös Loránd
University in Budapest, Hungary).
As a NSF postdoc at MIT, I was working with
Richard Stanley (still at MIT but also at University of Miami).
- Discrete and Polyhedral Geometry,
- Enumerative and Algebraic Combinatorics,
- Probability and Computations on Groups.
My book: Lectures on Discrete and Polyhedral Geometry.
Popular math writing links:
- Math 206B (Bijective Combinatorics, Winter 2021)
- Math 285(Computational Combinatorics, Fall 2022)
- Math 182 (Algorithms, Summer 2022)
- Math 184 (Enumerative Combinatorics, Spring 2022)
- Math 206B (Enumerative Combinatorics, Winter 2021)
- Math 218
(Probabilistic Method, Fall 2021)
- Math 285
(Discrete Geometry, Spring 2021)
- Math 180
(Graph Theory, Winter 2021)
(Convex Polytopes, Winter 2021)
- Math 206A
(Combinatorics of posets, Fall 2020)
- Math 285
(Combinatorics and Probability on Groups, Spring 2020)
- Math 19
(Integer Sequences Seminar, Fall 2019)
- Math 206B (Algebraic Combinatorics, Winter 2018)
- Math 206A (Discrete Geometry, Fall 2018)
- Math 206 (Combinatorics of integer sequences, Fall 2016)
Math 206 (Combinatorics of words, Fall 2014)
Math 285N (Tilings, Winter 2013)
Math 285N (Enumerative Combinatorics, Fall 2010)
Math 285N (Discrete Geometry, Spring 2010)
For other past courses, see my Teaching Page.
- Integer points in polytopes are hard to find, Mixed Integer Programming Workshop, USC, Los Angeles (May 24, 2023), slides only, Twitter thread.
- What do we know about the cogrowth sequence?, Transcendence and Combinatorics, IHP, Paris (Dec 9, 2022), slides only.
- Combinatorial inequalities, UIUC Colloquium (Sep 1, 2022),
- Complexity approach to combinatorial interpretations,
Open Problems in Algebraic Combinatorics Conference, Minneapolis (May 18, 2022),
talk video and slides.
- Combinatorial inequalities,
The Vinberg Lecture, Distinguished Lecture Series,
video and slides (May 4, 2022)
- Quantitative Linear Algebra,
IPAM Reunion workshop, UCLA, Lake Arrowhead, CA; slides only (Dec. 13, 2021).
Log-concave poset inequalities, see
Zoom talk video and
slides (CJCS, Nov 4, 2021).
linear extensions of posets, see Zoom talk video and
at the Permutations and Probability Banff workshop (Sep. 2021).
Hook formulas and their generalizations,
New Perspectives in Asymptotic Representation Theory (Sergei Kerov Memorial Conference),
POMI, St. Petersburg, Russia, see Zoom talk video on the website and slides (Aug. 2021).
Colloquium, Yale University, Zoom talk video
- Polyhedral domes, Colloquium,
Kings College London, UK, Zoom talk video
(this is a general audience talk, May 2021).
What is a combinatorial interpretation?,
Experimental Mathematics Seminar,
Rutgers (Apr. 2021). Zoom talk video
Sorting numbers, convex polytopes and geometric inequalities
(in Russian), 20th Modern Mathematics Summer School (Dubna, Russia, July 2021), video only.
Kronecker coefficients: bounds and complexity,
Triangle Lectures in Combinatorics,
UNC Greensboro (Nov. 2020). Zoom talk video
Domes over Curves, Polytopics:
Recent advances on polytopes, MPI (Apr. 7, 2021).
Zoom talk video and slides. Video of a blackboard version
of this talk is here, at NYU Geometry Seminar (Mar. 2023).
Counting Contingency Tables, Combinatorics Seminar, OSU (Sep. 2020).
Zoom talk video and slides.
- Counting with tiles, Combinatorics Seminar,
Paris 13 (June 2020). Zoom talk video
Counting linear extensions and Young tableaux,
BCC (July 2019),
Birmingham, UK. Slides only.
Complexity problems in enumerative combinatorics,
ICM Rio de Janeiro (Aug. 2018). Video and slides.
Tiling spaces with congruent polyhedra, Geometry Seminar,
Brown University (Dec. 2017). Slides only.
combinatorics and complexity of integer sequences, Banff workshop (Sep. 2017). Video only.
Computability and Enumeration,
Mathematics of Jirka Matousek, Charles University, Prague (July 2016). Video and slides.
in linear groups, random walks, automata and P-recursiveness, Banff, Canada (Mar. 2015). Video only.
Counting with Wang tiles,
IMA, Minneapolis (Nov. 2014). Video and slides.
theorems in Algebra and Geometry, Stony Brook U. (Sep. 2014). Video only.
For other (mostly older) lectures, see my Lectures Page.
I have a dated short (.pdf file, 1.5 pages)
and an extended (.pdf file, 34 pages)
versions of the resume.
I also have a dated list of my coauthors
with their web pages (if available).
Former Ph.D. students:
Department of Mathematics, UCLA
Los Angeles, CA 90095, USA
Office: Math Sciences 6125
Phone: (310) 825-4701 (no message service)
Fax: (310) 206-6673
E-mail: my last name AT math DOT ucla.edu
Last updated: 5/24/2023