Igor Pak Home Page
I am a Professor at the Mathematics Department
at UCLA. I am a member of the
Combinatorics Group,
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
MIT.
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:
- Discrete and Polyhedral Geometry,
- Enumerative and Algebraic Combinatorics,
- Probability and Computations on Groups.
My undergraduate advisor was
Alexandre
Kirillov (currently at
UPenn). My graduate advisor was
Persi Diaconis (currently at
Stanford). As a postdoc at Yale,
I was working with
László Lovász
(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).
My book: Lectures on Discrete and Polyhedral Geometry.
Popular math writing links:
Seminars:
Selected courses:
- Math 206B (Posets, Winter 2024)
- Math 206A (Convex Polytopes, Fall 2023)
- 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)
- IUM
(Convex Polytopes, Winter 2021)
- Math 206A
(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.
Selected lectures:
- Combinatorics and complexity of Stanley's inequality,
Stanley's birthday conference
(June 4, 2024), slides.
- Oda's strong factorization conjecture on stellar subdivision of triangulations (joint with Joaquín Moraga), slides only: Part 1 by Joaquín and Part 2 by me (May 2024).
- Combinatorics and computational
complexity of counting coincidences, GSCC'24 (Mar. 17, 2024), slides only.
- Equality cases of the Alexandrov-Fenchel inequality, Discrete Geometry workshop in Oberwolfach (Jan. 23, 2024).
- What is beyond D-finite?, video and slides at the
Computer algebra for functional equations in combinatorics and physics, IHP, Paris (Dec. 4, 2023).
- Poset inequalities, plenary talk at CanaDAM (June 8, 2023), slides only.
- 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),
slides only.
- 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).
-
Random
linear extensions of posets, see Zoom talk video and
slides
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).
-
Combinatorial Inequalities,
Colloquium, Yale University, Zoom talk video
and slides
(May 2021).
- Polyhedral domes, Colloquium,
Kings College London, UK, Zoom talk video
and slides
(this is a general audience talk, May 2021).
-
What is a combinatorial interpretation?,
Experimental Mathematics Seminar,
Rutgers (Apr. 2021). Zoom talk video
and slides.
-
Sorting numbers, convex polytopes and geometric inequalities
(in Russian), 20th Modern Mathematics Summer School (Dubna, Russia, July 2021), video only.
- Cogrowth sequences in groups and graphs,
ENS Group Theory Seminar (Jan. 2021),
Zoom talk video
and slides.
-
Kronecker coefficients: bounds and complexity,
Triangle Lectures in Combinatorics,
UNC Greensboro (Nov. 2020). Zoom talk video
and slides.
-
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
and slides.
-
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.
-
The
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.
-
Words
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.
-
Universality
theorems in Algebra and Geometry, Stony Brook U. (Sep. 2014). Video only.
For other (mostly older) lectures, see my Lectures Page.
Resume:
I have a dated short (.pdf file, 1.5 pages)
and an extended (.pdf file, 35 pages)
versions of the resume.
I also have a dated list of my coauthors
with their web pages (if available).
Former Ph.D. students:
Postdocs:
Olga Pak Graphic Design
Contact information:
Igor Pak
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: 7/29/2024