Nir Gadish
Research
Preprints
- Infinitesimal calculations in fundamental groups (with A. Ozbek, D. Sinha and B. Walter)
- (preprint) ArXiv:2403.20264.
- Letter-braiding: a universal bridge between combinatorial group theory and topology
- (preprint) ArXiv:2308.13635.
- A Serre spectral sequence for the moduli space of tropical curves (with C. Bibby, M. Chan and C. Yun)
- (preprint) ArXiv:2307.01960.
Publications
- Configuration spaces on a wedge of spheres and Hochschild-Pirashvili homology (with L. Hainaut)
- Annales Henri Lebesgue (accepted).
- Homology representations of compactified configurations on graphs applied to M2,n (with C. Bibby, M. Chan and C. Yun)
- Experimental Mathematics (2023): 1-13.
- Product Expansions of q-Character Polynomials (with A. Balachandran, A. Huang and S. Sun)
- Journal of Algebraic Combinatorics 57, no. 3 (2023): 975-1005.
- Correction to the article A spectral sequence for stratified spaces... (with D. Petersen)
- Geometry & Topology 25, no. 5 (2021): 2699-2706.
- Deletion and contraction in configuration spaces of graphs. (with S. Agarwal, M. Banks and D. Miyata)
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Algebraic & Geometric Topology (2021), DOI:10.2140/agt.2021.21.3663
- A generating function approach to new representation stability phenomena in orbit configuration spaces. (with C. Bibby)
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Transactions of the AMS, Series B 10, no. 09 (2023): 241-287.
- Combinatorics of orbit configuration spaces. (with C. Bibby)
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International Mathematics Research Notices, DOI:rnaa296 (2020).
- Adding points to configurations in closed balls. (with L. Chen, J. Lanier)
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Proceedings of the AMS (2019).
- Dimension-independent statistics of GL(n)$ via character polynomials.
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Proceedings of the AMS (2019).
- An explicit symmetric DGLA model of a bi-gon. (with I Griniasty and R. Lawrence)
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Journal of Knot Theory and Its Ramifications Vol 28, No. 11 (2019).
- A trace formula for the distribution of rational G-orbits in ramified covers, adapted to representation stability.
- New York Journal of Mathematics, Vol. 23 (2017): 987-1011.
- Categories of FI type: a unified approach to generalizing representation stability and character polynomials.
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Journal of Algebra, Vol. 480 (2017): 450-486.
- Representation Stability for Families of Linear Subspace Arrangements.
- Advances in Mathematics, Vol. 322 (2017): 341-377.
Not for publication
My Ph.D. thesis, titled: A general framework for representation stability, with applications to arrangements and arithmetic. Thesis Advisor: Prof. Benson Farb.
My topic proposal, on representation stability and applications to arithmetic statistics, under the supervision of Prof. Benson Farb.
My research project for a complex analysis graduate class at the University of Chicago: discussing the Ferrari cubic resolvent as a map between configuration spaces.
My undergraduate thesis, on a free DGLA model for the 2-cell. Thesis Advisor: Prof. Ruth Lawrence.
Teaching
- In 2024-2025 semesters, I am teaching Math 1070 (Mathematics of Change) at The University of Pennsylvania.
- In 2023-2024 semesters, I was the coordinator of the Lab of Geometry (Math 440) at The University of Michigan.
- In 2023-2024 semesters, taught Math 567 (Coding theory) at The University of Michigan.
- In 2022 Fall semester, I taught Math 490 (IBL Topology) in an Active Learning format at The University of Michigan.
- In 2022 Winter semester, I taught Math 310 (IBL Probability) in an Active Learning format at The Universiyy of Michigan.
- In 2021 Fall semester, I taught Math 115 (Calculus I) in an Active Learning format at The University of Michigan.
- In 2021 Winter semester, I taught recitations for Math 18.06 (Linear algebra) at MIT.
- In 2020 Fall semester, I taught Math 18.204 (Communications intensive course in discrete math) at MIT. See student projects here.
- In the 2018-2019 school year, I taught Math 15200-15300 (Calculus) at UChicago.
- In the 2017-2018 school year, I taught Math 15200 (Calculus), and served as a TA in the UChicago study abroad program in Paris.
- In the 2016-2017 school year, I taught Math 15300 (Calculus), 17600 (Basic Geometry (IBL)), and 19520 (Mathematical Methods for the Social Sciences) at UChicago.
- In the 2015-2016 school year, I taught Math 15100-15200 (Calculus), and 19600 (Linear Algebra) at UChicago.
- In the 2014-2015 school year, I was a College Fellow for Math 26700 (Representations of Finite Groups), 26200 (Point-Set Topology) , and 26300 (Algebraic Topology) at UChicago.
- In the 2011-2012 school year, I was a junior instructor for Math 114 and Math 157 (Applied Mathematics) at the Hebrew University of Jerusalem.
- In the 2010-2011 school year, I was a teaching assistant for Math 314 (Complex Valued Functions) at the Hebrew University of Jerusalem.
Notes
- Here are final projects that students wrote for my Communication Intensive course in discrete mathematics at MIT (Fall 2020).
- Here are notes in which I tried to understand what are algebraic functions (a long time ago).
- Here are notes and supplementary material that I wrote for my representation theory class.
- Here is an introduction and motivation to homology.
Representation theory supplementary material
18.204 (Fall 2020)
Final math communication projects from my (Fall 2020) 18.204 course at MIT - Communication intensive course on discrete mathematics:
- The polynomial method in incidence geometry.
[by Bryan Chen, Julia Wu, and Emily Xie]
- The probabilistic method.
[by Zhezheng Luo, Pachara Sawettamalya, and Yiwei Zhu]
- Ramsey theory.
[by Justen Holl, Elizabeth Tso, and Julia Balla]
- Machine learning and artificial intelligence.
[by Samuel Dorchuck, Amy Kim, and Abigail Moser]
- Applications of algebra to combinatorics.
[by Ellery Rajagopal, Fjona Parllaku, and Áron Ricardo Perez-Lopez]
Advice for 1st gen students (UNDER CONSTRUCTION!)
There are lots of hidden avenues for success in college, and students coming from non-academic backgrounds often go unaware that they are missing out. I've tried to compile a list of some opportunities that ambitious students should keep in mind. If you can think of others to add to this list, please send me an email!
- Formal Reading Courses:
You can get college credit for reading a book with a faculty advisor. This is a great opportunity to get one-on-one time with and learn from an experienced mathematician.
Benefits:
1) The faculty mentor has chance to get to know how you think and learn. When it comes time for you to ask for a recommendation letter, they can write insightfully and enthusiastically about your abilities.
2) You get to learn subjects that are not offered as standard courses (say, you want to learn about Mathematical Physics or Descriptive Set Theory), and you are not limited by the course offerings at your school.
3) Getting course credit will help you budget time for reading in your busy schedule. And you are very likely to get a good grade.
How to get started: if one of your teachers inspired you, walk up to them towards the end of the semester and ask whether they would be willing to mentor you through a reading course next semester. They might be too busy to do it themselves, but could sometimes direct you to other faculty members who are available and interested in taking a student like you.
- Directed reading program (DRP):
Some schools offer a DRP, whereby a graduate student mentors you though reading a textbook on a subject of your choosing.
How to get started:
Check with your math department whether they offer a DRP. You can also ask any graduate student, and hopefully they could direct you to relevant resources. Have a subject you wish to learn in mind. If you have a relationship with a graduate student, you can ask them directly to mentor you on a DRP.
- Research Experience for Undergraduates (summer REU):
A great way to spend your summer between academic years is to participate in an REU. These are programs offered by schools around North America and Europe, whereby *they pay you* to visit a school, learn mathematics, and engage in a research project.
Benefits:
1) You get to live for a few weeks in a different city, and you don't have to pay for the experience.
2) This is an opportunity to learn more math from experienced mentors, in addition to your standard courses.
3) You gain experience in independent study or in research. Such opportunities are typically hard to come-by, and are incredibly valuable.
4) An REU makes a wonderful addition to your CV, and will boost your chances to get into a good graduate school (if that's your goal).
5) You will meet peers with varied life experiences. Beyond the networking value, they might inform you of other opportunities to learn mathematics or otherwise build up your CV.
6) Your mentors could write you recommendation letters down the road.
How to get started:
There are many REUs opening every year all over the country. One place that aggregates many is the website
MathPrograms.org, but a quick Google search will surely direct you to many programs. You can also Google around for "Summer Schools in mathematics".
- Budapest Semester in Mathematics:
As the name suggests, this is a semester long enrichment program in Budapest, giving a feel for higher math research and learning. Some of the most successful students I've met participated in this program. It is very well known and reputable. And, I hear Budapest is a great city!
link
About me
I am an assistant professor at the University of Pennsylvania. My research interests lie in the interplay between algebraic topology, moduli problems, group theory and representation theory. Recently, I've been most interested in invariants of words in groups and their applications in low dimensional topology. Previously, I worked on representation stability phenomena in configuration spaces and moduli spaces.
Postal address
209 S. 33rd Street
Philadelphia,
PA
19104
USA
