I am currently a PhD student at Trinity College Dublin under the direction of Vladimir Dotsenko (09/2017-09/2021). I did 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. Or you just may not. Here's a picture of myself.
My curriculum vitae is available here. Last updated October 2020.
I am interested in homological algebra, homotopical algebra, algebraic homotopy, effective homology, higher structures, operads, representation theory and combinatorics.
- The Tamarkin--Tsygan Calculus of an algebra à la Stasheff. Accepted for publication at Homol. Homotopy Appl.
- Endofunctors and Poincaré–Birkhoff–Witt Theorems, with Vladimir Dotsenko. Published in Int. Math. Res. Notices, rnz369.
- Minimal models for monomial algebras. Accepted for publication at Homol. Homotopy Appl.
- Differential forms for smooth operadic algebras, with Ricardo Campos.
- A spectral sequence for tangent cohomology of algebraic operads, with José Moreno-Fernández. Submitted for publication.
- 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.
- The cohomology of twisted coalgebras. Submitted for publication. This article is based on my MSc thesis, which you can find a few lines below.
- Tangent complexes and the Diamond Lemma, with Vladimir Dotsenko.
- Homotopy quotients of non-commutative Batalin--Vilkovisky operads.
Upcoming and recent events
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.
- Visited Anton Khoroshkin and gave a talk at the Steklov Institute and at the HSE, November 2019, Moscow, Rusia.
- Visited Vladimir Dotsenko and gave a talk at l'Institut de Recherche Mathématique Avancée, November 2019, Université de Strasbourg, France.
- Visited Alexander Berglund and gave a talk at the University of Stockholm, 16-21 September 2019, Sweden.
- 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.
Talks and slides
- 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.
- The Tamarkin--Tsygan calculus of an algebra à la Stasheff. Algebraic Geometry Seminar at the HSE (Высшая школа экономики), Moscow, Russia. November 2019.
- Minimal models for monomial algebras. Shafarevich Seminar of the Steklov Mathematical Institute, Moscow, Russia. November 2019.
- The Tamarkin--Tsygan calculus of an algebra à la Stasheff. Institut de Recherche Mathématique Avancée, Université de Strasbourg, France. November, 2019.
- The Tamarkin--Tsygan calculus of an algebra à la Stasheff. Algebra and geometry seminar, University of Stockholm, Sweden. September, 2019.
- Pares exactos y una sucesión espectral de derivaciones. Seminario de Álgebra Homológica. Universidad de Buenos Aires, Argentina. July, 2019.
- Minimal models for monomial algebras. Homotopy meets homology, Trinity College Dublin, Dublin, Ireland. May, 2019.
- Minimal models for monomial algebras. Catégories supérieures, polygraphes et homotopie, L'IRIF, Paris, France. March, 2019.
- The Tamarkin--Tsygan calculus of an algebra à la Stasheff. Séminaire d'algèbre à l'IHP, Paris, France. March, 2019.
- An introduction to cohomology. PhD Journal Club, School of Mathematics, Trinity College Dublin, Ireland. November, 2018.
- Minimal models for monomial algebras. Seminar of the School of Mathematics, City London University, London, England. November, 2018.
- Minimal models for monomial algebras. Seminar of the School of Mathematics, National University of Ireland, Galway. October, 2018.
- Minimal models for monomial algebras. Higher dimensional rewriting and applications. Oxford, England. July, 2018.
- Cohomology of combinatorial species. Coloquio Latinoamericano de Álgebra. Quito, Ecuador. August, 2017.
I am/was a teacher assistant and/or graded for the following courses in TCD. Boldfaced courses are currently active. You may find further information by following the links provided. I also participated in MA4492, where students produced final year projects under the supervision of Vladimir Dotsenko.
Note that starting Michaelmas term 2019, course codes have
a new format! In particular, note course MA2323 has new code MAU22200 and new name.
- MA3428. Algebraic Topology II.
- MA341C. Seminar on Proofs from THE BOOK.
- MAU34102. Commutative Algebra.
- MA341D. Introduction to Groebner Bases.
- MAU33E01. Mathematics V.
- MA2323. Metric Spaces.
- 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.
Homework for MAU22101 (Michaelmas 2020)
The following are the questions and solutions for the
weekly assignments for MAU22101. Solutions due on and
uploaded weekly on Thuesdays at 4:00 pm. Assignments can
be found in the TEAMS channel for the class.
You may contact me at pedro at maths dot tcd dot ie.
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!
I am a casual blues and swing dancer, and you can find me either struttin' with the people of Downtown Blues or swinging out with the folks at Swing By. If you're curious, be sure to check their classes, there's always room for one more.
"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.