Marco Carfagnini

(he/him/his - they/them/their)

I acknowledge the Traditional Owners of country throughout Australia. I recognise the unique place held by Aboriginal and Torres Strait Islander peoples as the original custodians of country and their continued connection to the land, waterways, songlines and culture. I am fortunate to live and work on the land of the Wurundjeri and Boon Wurrung peoples. I acknowledge that sovereignty was never ceded.

I am a Lecturer (Assistant Professor) in the Stochastic Processes group at the School of Mathematics and Statistics at the University of Melbourne. My research is in stochastic analysis and its interplay with Lie groups and algebras, and functional analysis.

Previously, I was a Stefan E. Warschawski Visiting Assistant Professor at the University of California San Diego, mentored by Todd Kemp and Tianyi Zheng .

In September 2023 I was an IHES Invited Researcher at the Institut des Hautes Études Scientifiques in Paris, visiting Yilin Wang.

In Spring 2022 I was the Salgo-Noren Program Associate Fellow at the SLMath (former MSRI) in Berkeley.

I completed my PhD in June 2022 at the University of Connecticut under the supervision of Maria Gordina. Beofre that, I recevied my MS at the University of Rome Tor-Vergata, where I worked with Domenico Marinucci. You can find more about me in my curriculum vitae and by clicking the tabs below.

I strongly believe in the axioms of Federico Ardila:

Axiom 1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

Axiom 4. Every student deserves to be treated with dignity and respect.

Which Springer GMT book I would be (I wasn't too surprised by the outcome). Which one you would be.

If you are interested in applying for a PhD scholariship, please read here first.

Pedra da Gávea, Tijuca Forest, Rio de Janeiro, Brazil, July 2025

Email: marco dot carfagnini at unimelb dot edu dot au

Office: Peter Hall 139

Research

Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations, with Masha Gordina and Sasha Teplyaev, submitted. Arxiv, Pdf.
A note on small probabilities for spherical random fields at a critical regime, submitted. Arxiv, Pdf.
On the Onsager-Machlup functional for the Brownian motion on the Heisenberg group, with Masha Gordina, submitted. Arxiv, Pdf.
Small fluctuations for time-dependent spherical random fields, with Anna Paola Todino, 30: 1 - 25 (2025) . Arxiv, Pdf.
Spectral gap bounds on H-type groups, with Masha Gordina, accepted for publication in Contemp. Math. Volume 809, 2025 (New Trends in Sub-Riemannian Geometry) Arxiv, Pdf.
Onsager-Machlup functional for SLEκ loop measures, with Yilin Wang, Commun. Math. Phys. Volume 405, article number 258, (2024) Arxiv, Pdf.
Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content, with Masha Gordina, Int. Math. Res. Not. Volume 2024, Issue 3 (2024), 1894–1930, Arxiv, Pdf.
On the Support of a hypoelliptic diffusion on the Heisenberg group, ALEA-Lat. Am. J. Probab. Math. Stat. 20, (2023) 697–711, Arxiv, Pdf.
Small deviations and Chung's law of iterated logarithm for a hypoelliptic Brownian motion on the Heisenberg group, with Masha Gordina, Trans. Amer. Math. Soc. Ser. B 9 (2022), 322-342 . Arxiv, Pdf.
A functional law of the Iterated Logarithm for weakly hypoelliptic diffusions at time zero, with Juraj Foldes and David P. Herzog, Stoch. Process. Appl. 149 (2022) 188-223, Arxiv, Pdf.
An application of the Gaussian correlation inequality to the small deviations for a Kolmogorov diffusion, Electron. Commun. Probab. 27 (2022) n. 20, 1-7. Arxiv, Pdf.

Invited Talks

Conference PRIN GRAFIA (Geometry of RAndom FIelds and Applications), Il Palazzone di Cortona, Cortona, Italy, June 2025.
Probability Victoria, Online. April 2025.
Analysis Seminar, University of Melbourne, Melbourne, Australia, April 2025
Colloquium, Queen's University, Kingston, Canada, January 2025. Cancelled due to personal reasons.
PDE and Applications Seminar, Queen's University, Kingston, Canada, January 2025. Cancelled due to personal reasons.
Sub-Riemannian Analysis and Geometry, OIST Conference, Onna, Okinawa, Japan, January 2025. Cancelled due to personal reasons.
Banff Workshop on Stochastics and Geometry, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Canada, September 2024, video and slides.
Fourth Italian Meeting on Probability and Mathematical Statistics, special session on Random Fields, Rome, Italy, June 2024.
QuMA: Queer and Trans in Mathematical Analysis, Basque Center for Applied Mathematics, Bilbao, Spain, June 2024.
2024 Southern California Probability Symposium, California Institute of Technology , Pasadena, CA, April 2024.
Colloquium, The University of Melbourne, Melbourne, Australia, March 2024.
Probability Seminar, University College Dublin, Dublin, Ireland, December 2023.
Hunter College Math Colloquium, Hunter College, New York City, NY, December 2023.
RoMaDS, Rome Center on Mathematics for Modeling and Data Science, University of Rome Tor Vergata, Rome, Italy, September 2023.
Frontiers in Stochastic Analysis, University of Illinois at Chicago, Chicago, IL, August 2023.
Probability Seminar, Lehigh University, Bethlehem, PA, February 2023.
Third Italian Meeting on Probability and Mathematical Statistics, special session on Stochastic Processes and Geometry, Bologna, Italy, June 2022.
Joint Mathematics Meeting (JMM), special session on “Analysis on metric Spaces (a Mathematics Research Communities Session)”, Seattle, WA,(Online) April 2022.
AMS Special Session, Purdue University, IN, (Online) March 2022.
Harmonic Analysis and PDE seminar, University of Virginia (online), March 2022.
Probability Seminar, Pisa, Italy, July 2019.

Talks

Spectral Gap Bounds on H-Type Groups, 21st Northeast Probability Seminar, Columbia University, New York City, NY, November 2022.
Brownian motion on Lie groups and quasi-invariance, AGRS Junior Seminar, MSRI, Berkeley, CA, March 2022.
Small deviations and Chung’s laws of iterated logarithm for hypoelliptic Diffusions, 20th Northeast Probability Seminar, CUNY (Zoom talk), November 2021.
Random Facts, Series of talks in stochastic analysis and its connection to potential theory, functional analysis, and Lie algebras. Analysis Learning Seminar, University of Connecticut, Storrs, CT, October 2021.
Small deviations and Chung’s law of iterated logarithm for a hypoelliptic Brownian Motion on the Heisenberg Group, Banff Workshop on Stochastics and Geometry (Zoom talk), March 2021.
A Probabilistic Lagrangian, Math-Physics Learning Seminar, University of Connecticut (Zoom talk), September 2020.
Volume of Balls: from Euclidean spaces to Infinite Dimensions, Math-Club, University of Connecticut, Storrs, CT, February 2020.
Brownian Motion and Itô’s Integral, Analysis Learning Seminar, University of Connecticut, Storrs, CT, September 2019.
On the Onsager-Machlup functional for the Brownian motion on the Heisenberg Group, Second Italian Meeting in Probability and Mathematical Statistics, Vietri Sul Mare, Italy, June 2019.
Random Fields on Riemannian Manifold: The Gaussian Kinema5c Formula, Sigma Seminar, University of Connecticut, Storrs, CT, October 2018.

Service

Diversity, Equity, and Inclusion

Are you an LGBTQAI+ member working in a STEAM field? You might want to visit:
1. PATHS is a program to inspire and empower LGBTQ+ youth and young adults interested in careers in STEAM (science, technology, engineering, arts, and mathematics) fields through storytelling by current LGBTQ+ STEAM professionals, and connection to the resources needed to pursue STEAM careers. Go check my interview here!
2. Spectra, the Association for LGBT+ Mathematicians where you can find the Out and Ally list.
3. 500QueerScientists and my (a bit outdated) post here.
4. Lgbtstem, and my (a bit outdated) post here.
5. Mathématiqueer, here you can also find a list of LGBTQIA+ friendly math-conferences.
As a first-generation college student, I did not even know what a PhD program was when I started my undergrad. If you need any tips on how to apply for grad-school, waht's the academic carreer and life like, do not hesitate to shoot me an email.
In Spring 2019, together with other math grads, I founded a chapter of the Association for Women in Mathematics at the University of Connecticut.

Seminars

I organized the probability seminar probability seminar at UC San Diego for the a.y. 2023-2024.
In Fall 2020 and Spring 2021 Masha Gordina and I founded and organized the mathematical physics learning seminar.
In Fall 2019 I co-organized the Analysis Learning Seminar together with Matthew Badger.

Teaching

University of Melbourne

MAST20006: Probability for Statistics, SM I 2025.

MAST20004: Probability, Co-Teaching, SM I 2025.

University of California San Diego

Math 180C: Introduction to Stochastic Processes II, Spring 2024.

Math 180B: Introduction to Stochastic Processes I, Winter 2024

Math 180A: Introduction to Probability, Spring 2023, Fall 2023

Math 18: Linear Algebra, Fall 2022, Winter 2023.

University of Connecticut

Math 2410: Elementary Differential Equations, Spring 2020.

Math 2210: Applied Linear Algebra, Fall 2020.

Math 2110: Multivariable Calculus, TA, Fall 2019, Spring 2019.

Math 1071: Calculus for Business and Economics, Spring 2021.

Math 1132: Calculus II (TA) Fall 2018, Fall 2021.

Math 1131: Calculus I (TA) Fall 2017, Spring 2018.

Friends I talk math to

Morris Ang, University of California San Diego.

Paolo Badi, University of Rome Tor-Vergata.

Lucia Caramellino, University of Rome Tor-Vergata.

Lorenzo Dello Schiavo, University of Rome Tor-Vergata.

Juraj Foldes, University of Virginia.

Xi Geng, University of Melbourne.

Maria Gordina, University of Connecticut.

David P. Herzog, Iowa State University.

Todd Kemp, University of California San Diego.

Tai Melcher, University of Virginia.

Davide Parise, University of California San Diego.

Maurizia Rossi, University of Milano-Bicocca.

Alexander Teplyaev, University of Connecticut.

Anna Paola Todino, University of Piemonte Orientale.

Yilin Wang, ETH Zürich, Switzerland.

Tianyi Zheng, University of California San Diego.

Len Gross' (partial) academic family, Banff Research Center, September 2024. My academic family tree can be found at math-genealogy.

"Sei uno che per principio non s'aspetta più niente da niente [...] Tu sai che il meglio che ci si può aspettare è di evitare il peggio." Italo Calvino

"You're the sort of person who, on principle, no longer expects anything of anything [...] You know that the best you can expect is to avoid the worst". Translation by William Weaver.

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