Renan Gross

Background

I am a postdoctoral researcher of mathematics at the University of Cambridge, hosted by Wendelin Werner.
Before that, I did a postdoc at Tel Aviv University with Asaf Nachmias (2023-2024).
Before that I completed my PhD in mathematics at the Weizmann Institute of Science, under the supervision of Ronen Eldan (2023).
Before that I completed my masters in mathematics at the Weizmann Institute of Science (2017).
Before that I completed my undergraduate degree in mathematics and physics at the Technion (2015).
Before that I studied in the Israel Arts and Science Academy high school (2008).

I am interested in graph theory, probability, combinatorics, their union and their intersection.

The Boolean Zoo: This is a collaborative wiki whose purpose is to provide an extensive list of examples and counterexamples in Boolean function analysis. This is a (constant) work-in-progress; contributions are welcome!

Here is my blog. It contains expositions, technical explorations, random musings, and sometimes, plain nonsense.

Publications

The distance problem via subadditivty, R. Gross. arXiv 2025.

A sharp lower bound on the small eigenvalues of surfaces, R. Gross, Guy Lachman and Asaf Nachmias. arXiv 2024. A thorough exposition on the problem, the central concepts, and the proof.

Randomly twisted hypercubes: between structure and randomness, Itai Benjamini, Yotam Dikstein, R. Gross and Maksim Zhukovskii. Random Structures and Algorithms 2024. A user-friendly blogpost on the model and some basic techniques.

Noise sensitivity from fractional query algorithms and the axis-aligned Laplacian, R. Gross. arXiv 2022. A poster for the HALG 2022 conference. A presentation for the IMU student talks day 2022.

Brownian motion can feel the shape of a drum, R. Gross. Stochastic Processes and their Applications 2023. A poster for a local competition.

A phase diagram for bacterial swarming, Avraham Be'er, Bella Ilkanaiv, R. Gross, Daniel Kearns, Sebastian Heidenreich, Markus Bär and Gil Ariel. Communication Physics 3, 66 (2020). An introduction can be found here. The source code is available here.

Concentration on the Boolean hypercube via pathwise stochastic analysis, Ronen Eldan and R. Gross. Inventiones mathematicae 2022. Presented in STOC 2020. An introductory overview can be found here. For a crash course on Boolean functions, see here. A short animated lecture for STOC 2020 (recommended!). A longer, less animated one. Yet another one!

A conformal Skorokhod embedding, R. Gross. Electronic Communications in Probability Volume 24 (2019). A less-than-technical expository version can be found here. Slides for a talk at the 7th Weizmann Student Probability Day. A poster for the IMU meeting 2019 poster session. Design heavily inspired by Felix Breuer.

Decomposition of mean-field Gibbs distributions into product measures, Ronen Eldan and R. Gross. Electronic Journal of Probability Volume 23 (2018). An expository version can be found here. Slides for a talk at the IMU meeting 2018.

Exponential random graphs behave like mixtures of stochastic block models, Ronen Eldan and R. Gross. Annals of Applied Probability 2018, Vol. 28, No. 6, 3698-3735.

Indistinguishable sceneries on the Boolean hypercube, R. Gross and Uri Grupel. Combinatorics, Probability and Computing June 2018. A non-technical expository version can be found here. Slides for a talk given at the 6th Weizmann Student Probability Day.

Quasispecies in population of compositional assemblies, R. Gross, Itzhak Fouxon, Doron Lancet and Omer Markovitch. BMC Evolutionary Biology 2014 14:265. Slides, similar to those I used at the 27th ILASOL meeting.

Bounding the seed length of Miller and Shi's unbounded randomness expansion protocol, R. Gross and Scott Aaronson. arXiv 2014. An exposition can be found here.

Bridges, string art and Bèzier curves, R. Gross. +plus magazine, 2012. Also appears in The Best Writing on Mathematics 2013, Princeton University Press.

Summer School of Science

The Summer School of Science is an international summer science camp for high school students in Croatia. I have had the pleasure of leading a weeklong project there three times (1) (2) (3). This camp is a great opportunity for high-schoolers to do science and meet friends abroad, and I whole-heartidly recommend it.

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A note on the images:

• The upper left image shows a self-avoiding walk. The image is taken from the wikimedia commons and was made by the user Rocchini.
• The upper right image shows the output of a bacteria-tracking program I wrote in collaboration with Avraham Be'er. He studies the collective motion of bacteria, and you can read more about this work here.
• The lower left image shows a tiger deformed by a (mostly) analytic complex function. You can read more about this here.
• The lower right image shows a planar Brownian motion hitting a closed curve. The x-position of the motion has the uniform distribution on [-1,1]. See here for more.
• The center image shows me, crudely pasted onto a background of critical hexagonal percolation. The thick bold curve denotes a crossing alongside open sites.

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Background image from wikimedia commons by Erzbischof.

A very short biography

• 13.8 · 10⁹ BC: Universe created
• 2005 - 2008: Israel Arts and Science Academy
• 2008 - 2012: IDF
• 2012 - 2015: The Technion
• 2015 - 2023: The Weizmann Institute of Science
• 2023 - 2024: Tel Aviv University
• 2024 - ...: University of Cambridge

This section is under construction.

Fun

• My blog.
• I occasionally write and perform spoken word poetry. Here is my most popular piece amongst mathematicians:
  

  A complete playlist can be found here.

• I've played the piano since I was 11. Here is a video of the "Phrase Inversal" quartet in the Technion, of which I was a part, playing the first movement of Mozart's g minor quartet:

Contact

• Email: It is an ancient and respected tradition, for academics to "obfuscate" their email address. I am happy to follow that tradition:
  rg751 $you-know-the-sign$ cam.ac.uk