I am currently a visitor at the non-linear algebra research group of the MPIMiS in Leipzig. I completed my PhD at Trinity College Dublin under the direction of Vladimir Dotsenko (09/2017-09/2021). 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. Or you just may not. Here's a picture of myself.

My curriculum vitae is available here. Last updated December 2021.

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

I am currently giving a lecture series titled *Algebraic operads,
Koszul duality and Gröbner bases: an introduction* starting
on October 15th, 2021. More information and lecture notes here.

I joined the non-linear algebra research group of the MPIMiS in Leipzig on May 2021. After this, I will join the Institute for Mathematics at Humboldt Universität to work in the research group of Gaëtan Borot.

*The cohomology of coalgebras in species*. Published in Commun. Algebra.,*The Tamarkin--Tsygan Calculus of an algebra à la Stasheff*. Published in Homol. Homotopy Appl., no. 23(2) pp. 257-282.*Endofunctors and Poincaré–Birkhoff–Witt Theorems*, with Vladimir Dotsenko. Published in Int. Math. Res. Notices, rnz369.*Minimal models for monomial algebras*. Published in Homol. Homotopy Appl., no. 23(1) pp. 341-366.

*Generalized cohomological field theories in the higher order formalism*, with Vladimir Dotsenko and Sergey Shadrin.*Tangent complexes and the Diamond Lemma*, with Vladimir Dotsenko.*Differential forms for smooth operadic algebras*, with Ricardo Campos.*Resolutions of operads arising from Koszul (bi)algebras*. In peer review.*A spectral sequence for tangent cohomology of algebraic operads*, with José Moreno-Fernández.*Derived Poincaré--Birkhoff--Witt theorems*, with Anton Khoroshkin. Submitted for publication.*Finite generation for Hochschild cohomology of Gorenstein monomial algebras*, with Vladimir Dotsenko and Vincent Gélinas. Submitted for publication.

*Réunion annuelle du GDR de topologie algébrique.*26-29 October 2021, organized by Frédéric Chapoton and Vladimir Dotsenko.*TR Salento 2021 (School + Workshop on Topological Recursion).*6-17 September 2021, organized by the ReNewQuantum ERC Synergy Grant team at IPhT and IHES.*FNS-ANR OCHoTop Project: mid-term workshop.*July 5-7 2021, organized by Benoit Fresse and Kathryn Hess.*Higher structures and operadic calculus.*. 21-25 June 2021, organized by Bruno Vallette.*Viva Talbot!*A virtual Talbot Workshop retrospective. 1-6 June 2021, organized by Calista Bernard, Yajit Jain, Morgan Opie, Lucy Yang.*Cellular E_k-Algebras (hybrid meeting)*, at the Oberwolfach Institute. 23-29 May 2021, organized by Søren Galatius, Alexander Kupers and Oscar Randal-Williams.- Opening Workshop of the
*Higher Homotopical Structures programme*, at the Centre de Recerca Matemàtica (Bellaterra, Barcelona). 1-12 February 2021, organized by Imma Gálvez Carrillo. *Koszul duality & Operads*, 19-23 October 2020, organised by Noémie Combe and Geoffroy Horel.*Homology, graded algebras, infinity and Lie type structures*, 12-13 October 2020, organised by Natalia Iyudu. A workshop in memory of Viktor Nikolaevich Latyshev.*DG Methods in Commutative Algebra and Representation Theory*, 2-3 May 2020, Organised by Ben Briggs, Janina Letz, and Josh Pollitz. I talked about my preprint,*The Tamarkin--Tsygan calculus of an algebra à la Stasheff*.*Higher Homotopy Algebras in Topology 2*, 4-6 March 2020, Hamilton Mathematics Institute, Trinity College Dublin. I talked about my joint work with A. Khoroshkin,*Derived Poincaré--Birkhoff--Witt theorems*.*Interactions between algebra and geometry*, February 2020, IRMA, Strasbourg, France.*Homotopy meets homology*, 27-31 May 2019, Trinity College Dublin. Here's a photo of the bunch of us, at the stairs of the Hamilton Building.*Higher Homotopy Algebras in Topology 1*, May 9 - 10, 2019, Max Planck Institute for Mathematics at Bonn.*Higher Structures (Structures supérieures)*, 21-25 January 2019, CIRM, Luminy. Here's a photo of the hike to Morgiou.

*Differential operators of higher order and their homotopy trivializations*, Topology Seminar (University of Minnesota), organized by Calista Bernard and Alexander Voronov, November 2021.*Differential operators of higher order and their homotopy trivializations*, Mathematics Seminar, organized by Sergei Merkulov, November 2021.*Minimal models for monomial algebras*, LAGOON Seminar, organized by Frank Neumann and Sybille Schroll, October 2021.*The Diamond Lemma through homotopical algebra*, Leipzig seminar on Algebra, Algebraic Geometry and Algebraic Topology, organized by Daniele Agostini, Noémie Combe and Rainer Sinn, April 2021.*Tangent complexes and the Diamond Lemma*, Algebraic rewriting seminar organized by Cameron Calk, Cyrille Chenavier and Benjamin Dupont, May 2021.*Poincaré--Birkhoff--Witt theorems: homotopical and effective methods for universal envelopes.*, Algebra, Geometry and Physics seminar, organized by the MPIM Bonn and Humboldt Universität, March 2021.*Tangent complexes and the Diamond Lemma*, Séminaire et groupe de travail d’Algèbre of the LMPA Joseph Liouville (Lille), March 2021.*Tangent complexes and the Diamond lemma.*Opening Workshop of the Higher Homotopical Structures programme, at the Centre de Recerca Matemàtica (Bellaterra, Barcelona), organized by Imma Gálvez Carrillo. Recording available here.*Poincaré--Birkhoff--Witt theorems: homotopical and effective methods for universal envelopes.*Séminaire d'algèbre à l'Institut Henri Poincaré.*Poincaré--Birkhoff--Witt theorems: homotopical and effective methods for universal envelopes.*Algebra and topology seminar at the University of Copenhagen.*Differential forms for smooth affine algebras over operads.*EPFL Topology Seminar. November 2020.*Koszul duality in algebraic operads .*Deformation theory reading seminar at the University of Chicago. October 2020.*Algebraic operads.*Homological algebra seminar at the University of Buenos Aires. July 2020. Part II.- The non-commutative calculus of fields and forms through dg-resolutions. DG Methods in Commutative Algebra and Representation Theory, Special Zoom session. May 2020. A recording should be available soon.
*Derived Poincaré--Birkhoff--Witt theorems.*Higher Homotopy Algebras in Topology II, Hamilton Mathematics Institute, Trinity College Dublin. February 2020.*Derived Poincaré--Birkhoff--Witt theorems for algebras over operads. March 2020*Interactions between algebra and geometry, IRMA, Strasbourg, France. February 2020.

I was teacher assistant and/or graded for the following courses in TCD.

*MA3428.*Algebraic Topology II.*MA341C.*Seminar on*Proofs from THE BOOK*.*MAU34104.*Group Representations I.*MAU34102.*Commutative Algebra.*MA341D.*Introduction to Groebner Bases.*MAU33E01.*Mathematics V.*MA2323.*Metric Spaces.*MAU22E02.*Mathematics IV.*MAU22200*Advanced analysis.*MAU22101.*Group Theory.*MAU11202.*Advanced calculus.*MA1126.*Introduction to set theory and general topology.*MA1125.*Single-variable calculus and introductory analysis.*MAU11102.*Linear Algebra II.*MAU11101.*Linear Algebra I.

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

You may contact me at pedro at maths dot tcd dot ie.

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

*"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.
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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.