Roberto Pagaria

Roberto Pagaria

Research associate in Mathematics

I am a researcher in algebraic topology at Bologna university. Several articles published in leading math journals. Advanced knowledge of Abelian arrangements, configuration spaces, matroids, representation theory, spectral sequences and quiver varieties, acquired during thesis works and research activities.

Curriculum Vitae

Roberto Pagaria's CV

Articles and preprints

1. Representations of torsion-free arithmetic matroids, March 2021, (with G. Paolini) in European Journal of Combinatorics.
2. The cohomology ring of unordered configuration spaces of the torus, December 2020, in Algebraic & Geometric Topology.
3. Asymptotic growth of Betti numbers of ordered configuration spaces on an elliptic curve, May 2020, ArXiv:2005.02106.
4. Orientable arithmetic matroids, June 2020, in Discrete Mathematics.
5. Poincaré polynomial of elliptic arrangements is not a specialization of the Tutte polynomial , June 2020, in Discrete Mathematics.
6. On the cohomology of arrangements of subtori, January 2020, ArXiv:2001.05180 (with L. Moci).
7. Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements, November 2019, (with F. Callegaro, M. D'Adderio, E. Delucchi e L. Migliorini) in Transaction of AMS.
8. Erratum to ''Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements'' July 2020, (with F. Callegaro, M. D'Adderio, E. Delucchi e L. Migliorini) accepted in Transaction of AMS.
9. The homotopy type of elliptic arrangements, November 2019, ArXiv:1911.02905 (with E. Delucchi) accepted in Algebraic & Geometric Topology.
10. Two Examples of Toric Arrangements, October 2019, in Journal of Combinatorial Theory, Series A.
11. Combinatorics of Toric Arrangements, June 2019, in Rendiconti Lincei Matematica.
12. Cohomology of configuration spaces of surfaces, May 2019, ArXiv:1905.04724.
13. The Connection Between Combinatorics and Cohomology of Elliptic Arrangements, May 2018, ArXiv:1805.04906.

My Talks with slides:

• "Representation theory and configuration spaces" at Seminar on Combinatorics, Lie Theory, ​and Topology (recording ).
• "Wonderful models for toric arrangements" at the conference Arrangements at Home, I: Combinatorial Aspects (recording ).
• "Configuration spaces of surfaces" at Università degli Studi di Padova.
• "Orlik­-Solomon­ type presentations for the cohomology algebra of toric arrangements" at Heilbronn Institute (Bristol).
• "Unordered configuration spaces on surfaces" in the intensive research period Arrangements at Western.
• "Arithmetic Matroids and their Representations" at KTH Royal Institute of Technology.
• "Configuration spaces of points on surfaces" in Pisa at Baby Geometry (only abstract).
• "Toric Arrangements: An introduction between algebra, topology and combinatorics" at University of Bologna (only abstract).
• "Cohomology of configuration spaces of points on the 2-torus" at University of Neuchâtel.
• "Counting Regions" in Pisa at summer school PISA-HOKKAIDO-ROMA2 2018.
• "Combinatorics and Cohomology Algebra of Toric Arrangements" in Kyoto at the conference Matroids, Reflection Groups, and Free Hyperplane Arrangements.
• "Orlik-Solomon Relations for Toric Arrangements" in Dobbiaco/Toblach at the conference Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations II (2018).
• "Arrangiamenti Torici" in Cortona at the conference quinto incontro di COMBINATORIA DEI SISTEMI DI RADICI (no slides aviable).

Conferences in which I took part:

• Online Workshop Topological Complexity and Motion Planning.
• Virtual Workshop Arrangements at Home, II: Cohomology Jump Loci.
• Winter School Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations IV in Dobbiaco/Toblach.
• Winter School on Integrable Systems and Representation Theory in Bologna.
• Representation Theory In Venice.
• Algebraic Combinatorics in Genova.
• Summer School – New Perspectives in Hyperplane Arrangements in Bochum.
• New Trends in Topology and Geometry in Tunis.
• Groups & Algebras in Bicocca for Young algebraists in Milan.
• Winter School Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations III in Dobbiaco/Toblach.
• Topology of Arrangements and Representation Stability in Oberwolfach.
• Arrangements and beyond in Pisa.
• Perspective in Algebraic Topology in Pisa.
• Winter School Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations in Dobbiaco/Toblach.

Software developed:

Giovanni Paolini and I have developed "arithmat": a SageMath package to have fun with arithmetic matroids and integer matrices. It can be download from GitHub or PyPI.

Other documents:

• Phd thesis: Cohomology and Combinatorics of Toric Arrangements advisor Filippo Callegaro.
• Master thesis: Geometria delle varietà quiver with slides : advisor Andrea Maffei.
• 4th year colloquium at Scuola Normale Superiore: Decomposition formula for tensor product of representations of Lie algebras. Advisor prof. Andrea Maffei; a summary of the main topic.
• Bachelor thesis: Il gruppo di Brauer di un campo locale with slides, advisors Angelo Vistoli and Ilaria Del Corso.
• Un cruciverba per giocatori di go (an Italian crossword for go players).

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