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# Yan X Zhang's Academic Homepage

(If you can read that this is actually Greta's own poster, you don't need glasses)

This is the academic webpage of Yan Zhang (I publish under Yan X Zhang). I received my Ph. D. in mathematics at MIT under Richard Stanley in June 2013. Starting Fall 2013, I am a Morrey Visiting Assistant Professor at UC Berkeley. I do research in a variety of problems related to combinatorics, mostly algebraic.

If you are looking for more personal stuff, see my personal page.

## Current Activities (Spring 2016, UCB)

I am one of the co-organizers of the Berkeley Combinatorics Seminar, along with Lauren Williams and Khrystina Serhiyenko.

Currently teaching: Mathematics 185: Complex Analysis

## Papers

In roughly reverse-chronological order:
• On discrete cutting of cakes and maps (with Roberto Barrera, Kathryn Nyman, Amanda Ruiz, Francis Su). 2015. In preparation.
• Digital Convexity, Neural Codes, and Intervals (with Zvi Rosen). 2015. In preparation.

• Structural Theory of 2-d Adinkras (with Kevin Iga). 2015. Submitted.

A continuation of the earlier Adinkras work. We classify possible Adinkras under the additional constraints that come with 2 dimensions (1+1 space and time). As before, there are nice connections to doubly-even codes and the theory of graph switching.

• Four Variations on Graded Posets. 2015.

Explores four classes of graded posets, adding a nice observation of counting certain classes of combinatorial objects where switching between the exponential and ordinary generating functions is easy. Uses a lot of matrix tranfer methods. This was the work I took a hiatus on when I started working with Joel Lewis for graded (3+1)-avoiding posets; many similar techniques come up.

• The Combinatorics of Adinkras. 2013. MIT Thesis.

A more updated version of "Adinkras for Mathematicians." Contains some exposition and new results related to adinkras, a delightful combinatorial structure used to encode information about supersymmetry representations created by the "DFGHIL" collaboration. It has some neat results relating the combinatorics of adinkras to homological algebra, posets, coding theory, graph coloring, and so forth. I particularly like the elementary but cute idea of Stiefel-Whitney classes of codes.

• Enumeration of Graded (3+1)-Avoiding Posets (with Joel Lewis). Journal of Combinatorial Theory, Series A. 2013. Vol. 120, Issue 6.

This problem came out as a tangent to some enumeration techniques I was/am developing with posets. As a possible stepping stone in the difficult problem of enumerating (3+1)-avoiding posets, we successfully enumerate graded (3+1)-avoiding posets with generating function techniques.

The extended abstract presented to FPSAC 2012 in Nagoya, Japan can be found here. It won the award for best student paper.

• Adinkras for Mathematicians. Transactions of the American Mathematical Society. 366 (2014), 3325-3355.

Half of this paper is a mathematician (in particular combinatorialist) -targetting exposition of adinkras, a delightful combinatorial structure used to encode information about supersymmetry representations created by the "DFGHIL" collaboration of mathematicians and physicists. I then extract the purely combinatorial problems and make some structural and enumerative theorems using elementary poset-theoretical and homological techniques.

• Motors and Impossible Firing Patterns in the Parallel Chip-Firing Game (with Tian-yi Jiang and Ziv Scully). 2012. Preprint.

The parallel chip-firing game is an interesting dynamical system with some history that is far from well-understood. In this paper, we introduce the neat concept of "motors" to better study localized behavior of the game. Furthermore, we give the first complete characterization of the periodic behavior that can occur in this game.

• Separating hyperplanes of edge polytopes (with Takayuki Hibi and Nan Li). Journal of Combinatorial Theory, Series A, 120 (2013), 218-231.

We note the cute theme that certain properties (such as being an edge polytope, or normality) behave very well for edge polytopes when they are separated by hyperplanes. We make this precise and outline some related algorithms and structural properties.

• Matrices with restricted entries and q-analogues of permutations (with Joel Lewis, Ricky Liu, Alejandro Morales, Greta Panova, and Steven Sam). J. Combinatorics, 2 (2011), pp. 355-396 (issue 3).

This paper solves the problem of seeing if six graduate students can write a joint paper. It also uses a hodgepodge of ideas to look at enumerating matrices over finite fields with certain conditions. We think of them as q-analogues of permutations and explain strange coincidences. An earlier draft is available on the arXiv.

• The multidimensional Frobenius problem (with Jeffrey Amos, Iuliana Pascu, Vadim Ponomarenko, and Enrique Trevino). Involve, Vol. 4 (2011), No. 2, 187-197.

We generalize the Frobenius problem of determining the maximal integral value such that a given set of integral denominations cannot produce to higher dimensions. Many fundamentals we'd naturally want for such a theory are proven here.

## Talks and posters:

In roughly reverse-chronological order. Research talks refer to papers and will have no additional information. Other (such as expository) talks will contain an abstract or similar information.
• Adinkras, Progress and Problems, Shanghai Jiaotong University, 2015.
• Adinkras, Progress and Problems, UCLA, 2015.
• Adinkras, Progress and Problems, Minnesota, 2014.
• Similar to the "Adinkras for Mathematicians" talk, but includes more things as the program has advanced to 2 dimensions. Basically things from "Adinkras for Mathematicians" plus "Structural Theory of 2-d Adinkras."

• Combinatorics, Topology, and Fair Division, UC Berkeley MUSA Seminar, 2014.
• I talk about elementary topology with a combinatorial flavor applied to "real-life" problems such as splitting cakes or dividing rent, talking about Sperner's Lemma, Tucker's Lemma, and Brouwer's Fixed-Point Theorem.

• Patterns in the Chip-firing Game, Stanley@70, 2014.
• Adinkras for Mathematicians, San Jose State University, 2013.
• Adinkras for Mathematicians, San Francisco State University, 2013.
• Patterns in the Chip-firing Game, BAD Math Day, 2013.
• Variations on Graded Posets, Berkeley Combinatorics Seminar, 2013.
• Adinkras for Mathematicians, UC Davis Combinatorics Seminar, 2013.
• Variations on Graded Posets, MIT Combinatorics Seminar, 2012.
• Variations on Graded Posets, LaCim Combinatorics Seminar, 2012.
• A discussion of four problems where I give solutions of various forms: enumerating graded posets, graded (2+2)-avoiding posets, graded (3+1)-avoiding posets, and graded (2+2)- and (3+1)-avoiding posets. The (3+1)-avoiding poset work is joint work with Joel Lewis.

• Adinkras for Mathematicians, Dartmouth Combinatorics Seminar, 2012.
• Adinkras for Mathematicians, Berkeley Combinatorics Seminar, 2012.
• Pokerbots Lessons, MIT Pokerbots Competition, 2012.

During the MIT IAP period of 2011-2012, I worked about 14 hours a day (with Sasha Rush) to create a heads-up NL Hold'em program for the first MIT Pokerbots competition. We had some weird bugs but still won the dubious "Best Strategy Report" award. This was an invited lecture given for the second-year competitors about some lessons I learned, ranging from strategy to programming practices, but also some war stories of blood, sweat, and tears.

• Adinkras for Mathematicians, MIT Combinatorics Seminar , 2011.
• On Being Naive, MIT Applied Math Graduate Student Seminar , 2011.

A not-so random walk through some basic topics in probability and machine learning. I did this by juxtoposing some seemingly disparate topics that I bundle in my mental model: binary hypothesis testing, Naive Bayes (and its lesser-known sister, Noisy-Or), and basic causality concepts (e.g. d-separation). Theme: being naive is good.

• Matrices with restricted entries and q-analogues of permutations, FPSAC, 2011.
• Myths of Poker Mathematics, MIT Applied Math Graduate Student Seminar , 2011.
• I debunk some common misconceptions about the role of mathematics in poker, ranging from overemphasis ("all you have to do is play by the odds") to over de-emphasis ("poker is not about numbers, it is about guts"). In mathematician-style, I introduce successive toy games to show how certain "psychological" aspects such as bluffing arise naturally from game-theory and how different "action ranges" form given the players' options. The toy games are happily rich enough to create some heuristics directly applicable in actual play.

Abstract: I will attempt to illuminate the shady "umbral calculus" classically delegated to algebraic manipulations that annoyed mathematicians much like physics still does (in both senses of being dreadfully non-rigorous and delightfully useful), starting with Blissard's Symbolic Method which thrived in the 1860's development of classical invariant theory. The talk will then scan across a couple of other seemingly unrelated disciplines, including proving that \$e = 2\$ in finite calculus and giving a way to solve a general cubic/quartic. Short ninja lesson included upon request.

• On Permutation Avoidance, MAA/AMS Joint Meetings, 2006.

This is based on one of my projects at my REU in Duluth. I generalize slightly a result of Greene and contemplate another angle of thinking about permutation containment and avoidance by splitting permutations into classes based on RSK.

• The multidimensional Frobenius Problem, Young Mathematicians Conference, 2005.

## Teaching/Other:

All teaching and misc. activities go here. My teaching style and philosophy owe greatly to two great teachers: my mother and Sanjoy Mahajan.
• Recent Past Teaching:
• I am one of the co-organizers and instructors of SPARC, a different kind of summer camp for mathematically talented high school youth.
• I was a mentor at the first two years of MIT PRIMES. Mentees: Ziv Scully (chip-firing) and Aaron Klein (adinkras, graded posets).
• I mentored for RSI after being a participant back in 2002 (wow I'm old). Mentees: Damien Jiang (chip-firing) and Martin Camacho (posets).
• For math olympiad problem solving, I was an instructor/grader at the 2006 Math Olympiad Summer Program (MOSP) and the 2010 IDEA Math program.
• At MIT, I taught recitations (the second time as course administator) twice for 18.06 (Linear Algebra). I was also head grader for 18.310 (Principles of Discrete Applied Math).
• At Harvard, I taught sections for Math 25 (Honors Multivariable Calculus and Linear Algebra), Math 192r (Algebraic Combinatorics), and Math 115 (Methods of Analysis).

## Email:

Please send mathematics-related email to yanzhang (snail thing) math.berkeley.edu, and personal email to yanzhang (snail thing) post.harvard.edu.

## Misc

I founded and semi-regularly contribute to: Concrete Nonsense.