Ali K. Uncu

I finally caught a dear friend at RISC (Research Institute for Symbolic Computation) and asked for some of his wisdom. He answered in his usual unique and sometimes convoluted way. I hope you’ll enjoy our conversation as much as I did.

I get to catch up with a long-time friend in Linz, of all places. He was always someone to look up to since my graduate student years. I am happy to finally get to have a deep chat about some aspects of academic life with him.

Unfortunately, my camera died, and we didn’t get to record the last two minutes. We will keep those secrets for another day. Nevertheless, I hope you will enjoy the (incomplete) chat we had as much as I did. We will complete our conversation some other time.

 

I recently had the privilege of working on an interdisciplinary project. My coauthor, Michael, and I struggled to understand each other at first, but it became a fun project once the translations and goals were all set. Here is the published paper at JSC: https://www.sciencedirect.com/science/article/abs/pii/S0747717125000380, and here is my take on our collaboration at the Future Algorithms conference:

“Lange Nacht der Forschung” (Long Night of Research) is an Austria-wide inspiring bi-annual event that showcases the world of science and innovation to the public. Each institute and university holds events for one night after work hours all across Austria to meet the public and talk about their research. What questions are they asking? How is the research being conducted? Why is it important/interesting? What led the researchers to where they are? It is a celebration of knowledge. It bridges researchers and the broader community. It allows researchers to get out of their offices and labs for once and engage with people of all ages.

The Austrian Academy of Sciences asked the Johann Radon Institute’s contribution to this event. We were asked if we would like to spend one evening in Vienna at the Academy’s historic building and talk about some mathematics of our choice. I figured that this would be my last chance to join this event before my project ends at the Radon Institute and I volunteered to be a part of it. It was highly rewarding.

Outreach of mathematics is already difficult even when the knowledge level is given. Even between mathematicians, it is hard to understand the research of one another. Mathematicians specialize in difficult problems and end up joining the clique that is interested in similar questions. Each clique, over time, creates its own mathematics vocabulary, definitions, known results, lectures, and books; further making it hard to have a casual conversation on these abstract topics with history.

I would have loved to talk about integer partitions and q-series, but I made the stylistic choice and prepared some material on real quantifier elimination (what I have been working on in the project at the University of Bath). It offers more direct applications to everyday life, and I figured that would be easier to connect to people. Autonomous vehicles are a hot topic these days and the question “Computer, make sure these vehicle trajectories do not intersect” to avoid any collusion is a quantifier elimination problem when it is written in mathematics language.

Johann Radon Institute for Computational and Applied Mathematics room at this event was diverse and lots of fun. Other than my desk, we had rigidity theory, machine learning, cryptography and prime numbers, and various medical imaging exhibits.

I chatted not only with the locals but also with some tourists visiting Vienna. It was eye-opening. It barely felt like I was talking about mathematics. It was so rare that someone asked me how we were achieving what I said was the end goal (collision avoidance). People only wanted to see some faces and hear their enthusiasm for the work that they were doing. I should remember this for the next time I try to explain my research to my family. They don’t want details, they just want to know that I am enthusiastic about what I do. Anyway, it wasn’t all empty PR. We got a visit from the University of Vienna Mathematics student cohort. They asked me many technical questions. It was only then I launched GeoGebra Discovery and Maple and played with some examples I prepared beforehand.

It is always lovely to interact with the math enthusiasts. Türkiye Mathematik is one of the most established and active groups these days. They helped the SCALE 22 conference and provided the conference volunteers, to run the organızatıon smoothly. I am so glad they asked me to give a plenary talk and I was honored to provide such a colloquium on a topic I love.

If you know Turkish, if you would like to hear some Turkish, if you would like to listen to me give a mathematics talk in Turkish, here is me giving a birds-eye view of the Theory of Partitions:

I hope many more of these clubs will form and spread the love towards academics. I will try my hardest to say yes whenever they ask me for help.

November 21 – 25, 2022

This is a research in teams event that will take place at Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences (OEAW) and Research Institute for Symbolic Computation (RISC) of Johannes Kepler University (JKU). Some talks are announced below to introduce the problems and the state of the art.

This event is supported by Doktoral Program Computational Mathematics at JKU.

Organizers

• Veronika Pillwein (RISC JKU)
• Josef Schicho (RICAM OEAW, RISC JKU)
• Ali Kemal Uncu (RICAM OEAW, University of Bath)

Confirmed Participants

• Walter Bridges (Universität zu Köln)
• Sylvie Corteel (CNRS, Université Paris-Diderot)
• Jehanne Dousse (University of Geneva)
• Christian Krattenthaler (University of Vienna)
• Shunsuke Tsuchioka (Tokyo Institute of Technology)
• Ole Warnaar (University of Queensland)
• Zafeirakis Zafeirakopoulos (Gebze Technical University)

Talks: (Zoom Link: https://bath-ac-uk.zoom.us/j/6160978056)

• Zafeirakis Zafeirakopoulos, 21 Nov 2022 – 2pm @RICAM Seminar Room (SP2 416-2)
  Polyhedral Omega (+ Applications)
  Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities. Polyhedral Omega combines methods from partition analysis with methods from polyhedral geometry. In particular, we combine MacMahon’s iterative approach based on the Omega operator and explicit formulas for its evaluation with geometric tools such as Brion decomposition and Barvinok’s short rational function representations. This synthesis of ideas makes Polyhedral Omega by far the simplest algorithm for solving linear Diophantine systems available to date. After presenting the algorithm, we will see some applications and generalizations.
• Christian Krattenthaler, 22 Nov 2022 – 2pm @ RICAM Seminar Room (SP2 416-2) / Over Zoom
  Identities for cylindric Schur functions
  A well-known, but difficult-to-prove result is the determinantal formula for the sum of Schur functions over shapes with a restricted number of columns, due to Gordon, as realised by Bender and Knuth. I will represent affine refinements of these identities, which can be seen as identities for cylindric Schur functions.
  This is joint work with JiSum Huh, Jang Soo Kim and Soichi Okada.
• Ole Warnaar, 23 Nov 2022 – 2pm @ RISC Seminar Room
  Cylindric partitions
  Cylindric partitions are an affine analogue of plane partitions. They were first introduced in 1997 by Gessel and Krattenthaler, and are closely related to the representation theory of the affine Lie algebra . In this talk I will try to explain why cylindric partitions have become such a powerful combinatorial tool for discovering new identities of the Rogers–Ramanujan type.
• Jehanne Dousse, 24 Nov 2022 – 1:30pm @ RICAM Seminar Room (SP2 416-2) / Over Zoom
  Cylindric partitions and mod 8 Rogers-Ramanujan type identities
  Cylindric partitions, which were introduced by Gessel and Krattenthaler in 1997, can be seen as a generalisations of integer partitions involving periodicity conditions. Since the 1980s and the founding work of Lepowsky and Wilson on Rogers-Ramanujan identities, several connections between representation theory and partition identities have emerged. In particular, Andrews, Schilling and Warnaar discovered in 1998 a family of partition identities related to characters of A_2. Recently, Corteel and Welsh established a q-difference equation satisfied by generating functions for cylindric partitions, and used it to reprove the A_2 Rogers-Ramanujan identities of Andrews, Schilling and Warnaar. In this talk, we we build on this technique to discover and prove a new family of A_2 Rogers-Ramanujan identities with modulo 8 congruence conditions.
  This is joint work with Sylvie Corteel and Ali Uncu.
• Shunsuke Tsuchioka, 24 Nov 2022 – 2:45pm @ RICAM Seminar Room (SP2 416-2) / Over Zoom
  A Fibonacci variant of Rogers-Ramanujan identities via crystal energy
  We define a length function for a perfect crystal. As an application, we derive a variant of the Rogers-Ramanujan identities which involves (a q-analog of) the Fibonacci numbers.
• Shashank Kanade, 24 Nov 2022 – 4pm @ RICAM Seminar Room (SP2 416-2) / Over Zoom
  On the Andrews-Schilling-Warnaar identities
  Generalizing the usual Bailey machinery, Andrews-Schilling-Warnaar discovered an generalization of the notion of Bailey pairs and the Bailey lemma. Using this, they discovered identities involving principal characters of standard modules. However, for every positive integral level l (barring a few low-lying cases), a majority of identities involving level l standard modules were yet to be discovered. In a recent joint work with Russell, we have given conjectures that encompass all of the missing identities. Especially, we can prove our conjectures in levels 3 and 7 (and also levels 2, 4, 5, but these cases are not exactly new). Our proofs crucially use the Corteel-Welsh recursions governing cylindric partitions. Using a different circle of ideas, we were also able to produce various results when the levels are divisible by 3. In this talk, I will explain these developments. Time permitting, I will touch upon some exciting open problems that still remain.
• Walter Bridges, 25 Nov 2022 – 10am @ RICAM Seminar Room (SP2 416-2) / Over Zoom
  Weighted cylindric partitions and sum-product identities
  Corteel and Welsh recently showed how sum-product identities arise naturally from cylindric partitions.  Using work of Han and Xiong, we extend their ideas to more general structures like weighted cylindric partitions, symmetric cylindric partitions and skew double-shifted plane partitions.  In this greater generality, “all products” appear.  We discover new identities and reprove the Göllnitz–Gordon and Little Göllnitz identities, as well as some so-called Schmidt-type partition identities highlighted in recent work of Andrews and Paule. 
  This is joint work with Ali Uncu.
• Ali Uncu, 25 Nov 2022 – 2pm @ RICAM Seminar Room (SP2 416-2) / Over Zoom
  On modulo 11 and 13 cylindric partition conjectures of Kanade-Russell
  In this concluding (and to be informal) talk, I will show how we recently proved Modulo 11 and 13 cylindrical partition related conjectures of Kanade-Russell.