Below you will find information about my current graduate students and my graduate student advising policies and practices (keep scrolling for undergraduate advising). If you are a graduate student interested in working with me, you should do the following (items 2 and 3 below may be permuted, but item 1 should come first and item 4 last):

- Read this web page.
- Talk with one (or more) of my graduate students about what it is like to work with me.
- Glance through one (or more) of my recent papers to see if they look interesting to you.
- Stop by my office to discuss a reading course sometime on a Monday, Wednesday, or Friday.

In general, I will not take on more than 4.0 students at a given time, where the student weight function is 1.0 for graduate students, 1.5 for postdocs, and 0.5 for undergraduate students or co-advised graduate students. I try to adhere to this limit to ensure that I have adequate time for all of my students while still maintaining my own research program and sanity.

**Ezgi Kantarci Oguz**(Ph.D. expected 5/2018) studies shifted combinatorics and specializes in counter-examples. She has found ways to transfer many nice combinatorial constructions that exist in type A to natural constructions in type B. Her growing list of papers includes the following:- Ezgi Kantarci Oguz,
*A Note on Jing and Li's Type B Quasischur Functions*, Annals of Combinatorics (to appear). arXiv:1703.09358 - Ezgi Kantarci Oguz,
*A Type B Analogue to Ribbon Tableaux*, submitted 2017. arXiv:1701.07497 - Sami Assaf and Ezgi Kantarci Oguz,
*Crystal graphs for shifted tableaux*, Séminaire Lotharingien de Combinatoire (to appear as part of FPSAC 2018 conference proceedings). arXiv:1802.07352 - Sami Assaf and Ezgi Kantarci Oguz,
*A local characterization of crystals for the quantum queer superalgebra*, in preparation.

- Ezgi Kantarci Oguz,
**Nicolle Sandoval Gonzalez**studies Demazure modules and their connections with nonsymmetric Macdonald polynomials. She also works on problems in categorification with Professor Aaron Lauda. Her growing list of papers includes the following:- Sami Assaf and Nicolle S. Gonzalez,
*Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials*, Séminaire Lotharingien de Combinatoire (to appear as part of FPSAC 2018 conference proceedings).

- Sami Assaf and Nicolle S. Gonzalez,
**Danjoseph Quijada**studies type A Demazure characters, also called standard bases or key polynomials, from a combinatorial perspective. His growing list of papers includes the following:- Sami Assaf and Danjoseph Quijada,
*A Pieri rule for key polynomials*, Séminaire Lotharingien de Combinatoire (to appear as part of FPSAC 2018 conference proceedings).

- Sami Assaf and Danjoseph Quijada,
**Ye Qiu**studies graph theory. He is co-advised by Professor Shang-Hua Teng in the Computer Science department.

If you are a graduate student considering working with me, then the first step is to set up a reading course. This gives us an opportunity to work together and gives you a hands-on introduction to the area in which I work. Any one of the following excellent graduate texts would be suitable for a reading course:

**Symmetric functions**- I. G. Macdonald,
*Symmetric Functions and Hall Polynomials*. This is the definitive encyclopedia on symmetric function theory. - Richard Stanley,
*Enumerative Combinatorics, Volume II*. Chapter 7 features a thorough treatment of classical symmetric function theory, with more examples and combinatorial constructions than Chapter I of Macdonald.

- I. G. Macdonald,
**Representation theory**- William Fulton,
*Young Tableaux: With Applications to Representation Theory and Geometry*. This excellent text has three sections, the first an elementary introduction to algebraic combinatorics, the second a combinatorial construction for representations of symmetric and general linear groups, and the third an advanced study in Schubert calculus. - Bruce Sagan,
*The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions*. A thorough guide to combinatorial representation theory that builds more theory than Fulton while maintaining a concrete approach.

- William Fulton,
**Algebraic geometry**- I. G. Macdonald,
*Notes on Schubert polynomials*. Macdonald's unpublished notes give an encyclopedic treatment of Schubert polynomials, cleaning up many classical results of Lascoux and Schutzenberger. - Laurent Manivel,
*Symmetric Functions, Schubert Polynomials and Degeneracy Loci*. I have not read this yet, but I really should. It is regarded as a solid introduction to Schubert polynomials.

- I. G. Macdonald,

A good way to learn about the broader area of Combinatorics is by attending the USC Combinatorics Seminar. In addition to external speakers, each semester several faculty and postdocs at USC present on their current research. Talks are generally accessible to first year graduate students.

Occasionally I advise strong undergraduate mathematics majors in independent research projects in Combinatorics. If you are interested in working with me, please know that this will happen only if all of the following conditions are met:

- I have a suitable research project available.
- I have not reach my 4.0 student limit (see Graduate student advising).
- You have taken and enjoyed Math 410, and (at least) one of Math 432 or Math 470.
- You stop by my office to discuss math sometime on a Monday, Wednesday, or Friday.

**George Wang**(Spring 2015 -- Spring 2016) studied enumeration of Young tableaux. His research project culminated in a research paper, and he was awared a National Science Foundation Graduate Research Fellowship to pursue a Ph. D. in mathematics at the University of Pennsylvania:- George Wang,
*Enumerating quasi-Yamanouchi tableaux of Durfee size two*, arXiv:1610.04206

- George Wang,
**Sabrina Enriquez**(Fall 2017) studies reduced words for permutations. She plans to pursue a Ph. D. in mathematics beginning next year.

This clip is from a 2016 interview with USC's Undergraduate Research Consortium about my research and how I incorporate undergraduate students into my research group. George Wang also appears in the video.

This clip came from a 1 hour workshop on applying to graduate school that I gave during a visit to my undergraduate alma matar, the University of Notre Dame, in 2014. While I am clearly biased, I do believe that it has some good advice for undergraduate students planning to apply to graduate programs.

For children ages 4-5, I also organize the Venice Math Circle. We currently have capactity for five children, but hope to expand in the near future.