# Pedro Tamaroff

I am currently a postdoctoral researcher based in Humboldt-Universität zu Berlin and working in the research group of Gaetan Borot. I completed my PhD at Trinity College Dublin under the direction of Vladimir Dotsenko. My dissertation is available here. I completed my undergraduate studies at the University of Buenos Aires, and wrote my thesis under the direction of Mariano Suárez-Álvarez. You may know me from math.SE, where I am a moderator. Here is a picture of myself.

My curriculum vitae is available here. Last updated December 2022.

## Research interests

I am interested in homological algebra, homotopical algebra, algebraic homotopy, effective homology, higher structures, operads, representation theory and combinatorics.

## CIMPA School 2023

I was part of the organizing committee of the 2023 CIMPA School Crossroads of geometry, representation theory and higher structures, which took place from March 13th to March 26th 2023 in Puerto Madryn, Argentina, and which was a great success. More information available here.

## News

I was a postdoctoral researcher at the non-linear algebra research group of the MPIMiS in Leipzig from May 2021 to March 2022. During my stay there, I gave a lecture series titled Algebraic operads, Koszul duality and Gröbner bases: an introduction from October 15th 2021 to January, 21st 2022. More information and lecture notes here.

## Publications

1. Generalized cohomological field theories in the higher order formalism, with Vladimir Dotsenko and Sergey Shadrin. Published in Communications in Mathematical Physics.
2. Derived Poincaré--Birkhoff--Witt theorems, with Anton Khoroshkin and an appendix by Vladimir Dotsenko. Published in Letters in Mathematical Physics.
3. FG for Hochschild cohomology of Gorenstein monomial algebras, with Vladimir Dotsenko and Vincent Gélinas. Published in Selecta Mathematica.
4. Resolutions of operads via Koszul (bi)algebras. Published in J. Homotopy Relat. Struct.
5. The cohomology of coalgebras in species. Published in Commun. Algebra.
6. The Tamarkin--Tsygan Calculus of an algebra à la Stasheff. Published in Homol. Homotopy Appl., no. 23(2) pp. 257-282.
7. Endofunctors and Poincaré–Birkhoff–Witt Theorems, with Vladimir Dotsenko. Published in Int. Math. Res. Notices, rnz369.
8. Minimal models for monomial algebras. Published in Homol. Homotopy Appl., no. 23(1) pp. 341-366.

## Preprints

1. Tangent complexes and the Diamond Lemma, with Vladimir Dotsenko.
2. Differential forms for smooth operadic algebras, with Ricardo Campos.
3. A spectral sequence for tangent cohomology of algebraic operads, with José Moreno-Fernández.

## Upcoming and recent events

1. Groups, Rings and the YBE. 18-23 June 2023, Blankenberge, Belgium.
2. Operads in Málaga: a workshop in operad theory. 23-27 January 2023.
3. Geometric and comb. methods in homol. algebra. 20-22 July 2022, Aarhus.
4. Barcelona Conference on Higher Structures. 13-17 June 2022.
5. Réunion annuelle du GDR de topologie algébrique. 26-29 October 2021.
6. Topological Recursion in Salento. 6-17 September 2021.
7. FNS-ANR OCHoTop Project: mid-term workshop. 5-7 July 2021.
8. Higher structures and operadic calculus.. 21-25 June 2021.
9. Viva Talbot! A virtual Talbot Workshop retrospective. 1-6 June 2021.
10. Cellular $E_k$-Algebras, at the Oberwolfach Institute. 23-29 May 2021.
11. Higher Homotopical Structures at CIRM Barcelona. 1-12 February 2021.

## Recent talks and slides

1. Differential operators of higher order and their homotopy trivializations, at the Minnesota Topology Seminar, November 2021.
2. Differential operators of higher order and their homotopy trivializations. Luxembourg Mathematics Seminar, November 2021.
3. Minimal models for monomial algebras, LAGOON Seminar, October 2021.
4. The Diamond Lemma through homotopical algebra, MPIMiS Leipzig, April 2021.
5. Tangent complexes and the Diamond Lemma, Algebraic rewriting seminar, May 2021.
6. Poincaré--Birkhoff--Witt theorems: homotopical and effective methods for universal envelopes., Algebra, Geometry and Physics seminar, March 2021.
7. Tangent complexes and the Diamond Lemma, Séminaire et groupe de travail d’Algèbre, March 2021.
8. Tangent complexes and the Diamond lemma. HHS at CIRM. Recording available here.

## WiSe 2023 at Humboldt

I am teaching Representation Theory of Finite Groups and Algebras during WiSe 2023. More information available here.

## Past teaching

I was teacher assistant and/or graded for the following courses in Trinity College Dublin.

1. MA3428. Algebraic Topology II.
2. MA341C. Seminar on Proofs from THE BOOK.
3. MAU34104. Group Representations I.
4. MAU34102. Commutative Algebra.
5. MA341D. Introduction to Groebner Bases.
6. MAU33E01. Mathematics V.
7. MA2323. Metric Spaces.
8. MAU22E02. Mathematics IV.
10. MAU22101. Group Theory.
12. MA1126. Introduction to set theory and general topology.
13. MA1125. Single-variable calculus and introductory analysis.
14. MAU11102. Linear Algebra II.
15. MAU11101. Linear Algebra I.

## Notes

1. Algebraic operads, Koszul duality and Gröbner bases: an introduction. Lecture notes for the Winter Lecture Series 2021-2022 at MPIMiS. Appendix pending.
2. Little disks operads and configuration spaces. Talbot 2021 (A virtual Talbot Workshop retrospective ). Notes for Najib Idrissi's talk on Talbot 2015.
3. An introduction to cohomology. PhD Journal Club, School of Mathematics, Trinity College Dublin, Ireland. November, 2018.
4. Cohomology of combinatorial species. Slides for the Coloquio Latinoamericano de Álgebra. Quito, Ecuador. August, 2017.
5. Cohomology of combinatorial species. Tesis de Licenciatura, Universidad de Buenos Aires, Argentina (Introduction in Spanish).
6. Análisis Complejo. In Spanish. Unfinished set of notes for an undergraduate course at Universidad de Buenos Aires. Comments are welcome!
7. Rational and D-finite power series. Model notes for students of MA4492, Hilary Term 2017, Trinity College Dublin, Ireland.
8. The pigeon-hole principle and double counting. Model notes for students of MA341C, Michealmas Term 2018, Trinity College Dublin, Ireland.

## Contact me

You may contact me at tamarofp at hu dash berlin dot de. The email tamaroff at mis dot mpg dot de is no longer active.

## Some art I like

These are some comics by False Knees. You can buy prints here if you like them, or see more in their Instagram account!

## Quotes

"We all come from somewhere. We carry that place with us wherever we go. That never leaves our heart. Not entirely. But none of us can predict where our voyage will lead. We may suffer losses along the way. But we can hope to learn and grow from those experiences and from those who accompany us in our journey." Saru in The Sound of Thunder.

"Connection, joy, love, and resurrection: with these words, the path becomes clear for a moment, and then disappears. If I have a path I am still searching for it. We all are. That's how we find our way. By choosing to walk forward. Together. And if there is a greater hand leading us into uncertain future I can only hope it guides us well." Michael Burnham in Saints of Imperfection.

"We are deeply social and deeply instinctual animals, so much that our well-being depends on many things we do that are hard to explain in an intellectual way. That is why you do well to follow your heart and your passion. Bare reason is likely to lead you astray. None of us are smart and wise enough to figure it out intellectually." Bill Thurston in this MO post.

"Attention is the reader's gift to you. That gift is precious. And finite. And should you fail to be a respectful steward of that gift—most commonly, by boring or exasperating your reader—it will be promptly revoked.

"Once a reader revokes the gift of attention, you don't have a reader anymore. Then you become a writer only in the narrowest sense of the word. Yes, you put words on some pages. But if your reader has disappeared, what was the point? How is your writing more valuable than a random string of characters? Like the proverbial tree falling in the woods, no one's there to notice the difference." Matthew Butterick in his book on typography.