Marcelo Mendes Disconzi

Department of Mathematics, Vanderbilt University

email: marcelo.disconzi at vanderbilt.edu

office: Stevenson Center 1515

phone: (615) 322 7147

mail to: 1326 Stevenson Center Ln, Vanderbilt University, Nashville TN 37240

Department of Mathematics, Vanderbilt University

email: marcelo.disconzi at vanderbilt.edu

office: Stevenson Center 1515

phone: (615) 322 7147

mail to: 1326 Stevenson Center Ln, Vanderbilt University, Nashville TN 37240

Notes, links, and media

General

Here you will find some notes, links, and media materials (e.g., videos of seminars).

Here you will find some notes, links, and media materials (e.g., videos of seminars).

Notes

Here are some notes that I (and other people) have written. For my class notes, see my teaching page.

Here are some notes that I (and other people) have written. For my class notes, see my teaching page.

Causality, local well-posedness, and all that. Notes
of a talk I gave in program The Many Faces of Relativistic Fluid Dynamics at the Kavli Institute for Theoretical Physics, UC Santa Barbara, June 2023. This is a non-technical introduction to the topic aimed at an audience of physicists. Here is a video of the talk.

Recent developments in relativistic fluids. These are notes that grew out of a series of lectures I gave at
the semester program General Relativity, Center of Mathematical Sciences and Applications, Harvard University, May 16-17, 2022 (here is a video of the lectures; second video here), and at the Advanced Studies Institutes (ASI) in Uzbekistan,
part of the USA-Uzbekistan Collaboration for Research, Education and Student Training, July 25-August 4, 2022.

The Classical Gauge Theoretic Structure of the Standard
Model. This is an undergraduate senior thesis which I supervised by
Elijah Sheridan. It provides a helpful "dictionary" for mathematicians
to understand the basic constructions and concepts of classical gauge theory
used by physicists in the standard model.

Introduction to nonlinear
wave equations. Short introduction to the topic by Jonathan Luk.

General relativity. Introduction to mathematical general relativity from a modern perspective by Stefanos Aretakis.

Introduction to microlocal analysis. Introduction to the topic by Peter Hintz.

Recent
developments in the theory of relativistic fluids. Notes
of a series of lectures I gave at the Summer
School on Recent Advances in Mathematical Fluid Dynamics, May
20-24, 2019, at USC. Here
is a .zip file with the .tex, .bbl, and pictures of the notes. People
are welcome to download, modify, and use the .tex file as they see fit
(and here
are the handwritten notes, just in case). Here
is some extra material that complements the notes. Other topics covered
in the summer school were Non-uniqueness of weak solutions to the Euler
and Navier-Stokes equations, by
Tristan Buckmaster, Recent developments on water waves, by
Yu Deng, and Nonlinear dynamics of the Schrodinger equations with
periodic boundary conditions, by
Emanuele Haus.

Recent advances in classical and relativistic fluids. Notes of a
series of lectures I gave at the summer school Boston
City Limits 2018, June 11-21, at MIT.
Here is a .zip
file with the .tex, .bbl, and pictures of the notes. People are welcome
to download, modify, and use the .tex file as they see fit (and here
are the handwritten notes, just in case). Other topics covered in the
summer school were mathematical general relativity, by Stefanos
Aretakis (notes here),
the formation of singularities in general relativity, by Jared
Speck (notes TBP), and solitions, bubbling, and blow-up for
semilinear PDEs, by Andrew
Lawrie (notes here).

Some advanced
techniques on PDEs. I review how negative-norm Sobolev
spaces can be used to derive a necessary and sufficient condition for
existence of weak solutions of any linear PDE. Using this, I then show
Egorov's example of a PDE that is not locally solvable at the origin.
Some further applications are derived.

Holographic
renormalization. Notes of a talk I gave in the RTG
Seminar in Geometry and Physics at Stony Brook.

Correlation
functions in QFT. (Handwritten notes.) The basic ideas and concepts of
quantum field theory are discussed with the intent of making physics
books and papers on the subject more accessible to a mathematical
audience. The focus is on correlation functions for the scalar field:
what they are, how to compute them, their Feynman diagrams and
renormalization properties. For a more details, see the table
of contents.

Elementary
realization of of BRST symmetry and gauge fixing. Notes of a
series of lectures given by Martin
Rocek. All ideas of BRST symmetry and BV formalism are developed
at a very basic level using finite dimensional integrals instead of path
integrals. Excellent for those interested in the general idea of the
formalism.

Some algebraic
structures in physics. Notes from a series of informal meetings
that I and some other students organized with the goal of sharing our
different background in physics and mathematics.

Some ideas in Conformal Field
Theory. Notes from a talk I gave in the RTG
Seminar in Geometry and Physics at Stony Brook (.zip file with a
bunch of .jpg files, or click here
to access each file separetely).

Spontaneous
symmetry breaking. - Introductory notes on the Higgs mechanism.

Mathematical
Foundations of Classical and Quantum Field Theory. Notes of two
summer courses I took on the subject. I took these notes before starting my PhD and in hindsight
I would have written things differently. But perhaps precisely because of that some uninitiated
student might benefit from them. For a sharper introduction to the topic, see
Elijah's notes above.

Media and outreach

From free-boundary fluids to the constraint equations. Video of a talk I gave in the workshop Mass, the Einstein Constraint Equations, and the Penrose Inequality Conjecture at the Simons Center for Geometry and Physics, jointly with the colloquium of the Stony Brook Department of Mathematics, (2023).

Causality, local well-posedness, and all that. Video of a talk I gave in the program The Many Faces of Relativistic Fluid Dynamics at the Kavli Institute for Theoretical Physics, UC Santa Barbara (2023).

Here is a Vanderbilt
news story on the occasion of my Chancellor's
Faculty Fellowship award (2023).

General-relativistic viscous fluids. Video of a talk I gave at the
General Relativity Seminar,
Center of Mathematical Sciences and Applications, Harvard University (2022).

A brief overview of recent developments in relativistic fluids.
Video of
a six-hours series of lectures at the semester program General Relativity, Center of Mathematical Sciences and Applications, Harvard University (2022). Click here for the second video.

General-relativistic viscous fluids. Video of a
talk I gave in the
General Relativity Conference, Center of Mathematical Sciences and Applications, Harvard University (2022).

Here is a news story by
the Illinois Center for Advanced Studies of the Universe at UIUC,
describing my work First-order General Relativistic Viscous Fluid Dynamics (2022), written with
Fabio S. Bemfica and Jorge
Noronha
(2022).

Here is
Vanderbilt news story about a NSF Research Trainee award for which I am a Co-Principla Investigator together with Principal
Investigator
Kelly Holley-Bockelmann. The goal is to establish a graduate certificate program in the emerging field of multimessenger astronomy (2022).

General-relativistic viscous fluids. Video of a
talk I gave at the
Princeton Gravity Initiative,
Princeton University (2021).

General-relativistic viscous fluids. Video of a
talk I gave in the Workshop on QGP Phenomenology (2021).

The relativistic Euler equations with a physical vacuum boundary. Video of a talk I gave at the
Rocky Mountain Mathematical Physics Seminar,
University of Colorado Boulder (2021).

General relativistic viscous fluids. Video of a talk I gave at the
Colloquium of the Zu Chongzhi Center for Mathematics and Computational Sciences,
Duke Kunshan University (2021).

The relativistic Euler equations with a physical vacuum boundary. Video of a talk I gave in the
Center for Nonlinear Analysis
at Carnegie Mellon University (2021).

General-relativistic viscous
fluids. Video of a talk I gave in the workshop Relativistic
Hydrodynamics: Foundations, Novel Applications and Interdisciplinary
Connections that was jointly organized by the
Gravity, Quantum Fields and Information group at the Max
Planck Institute for Gravitational Physics (Albert Einstein Institute)
and the Illinois Center for
Advanced Studies of the Universe. Click here
for the slides of the talk. Here is a discussion session of the workshop; the discussion of my talk starts at 21:57min (2020).

General-relativistic viscous
fluids. Video of a talk I gave in the workshop Mathematical
and Computational Approaches for the Einstein Field Equations with
Matter Fields that took place at the Institute
for Computational and Experimental Research in Mathematics (ICERM)
in Providence, RI. Click here
for the slides of the talk (2020).

General-relativistic viscous
fluids. Video of a talk I gave in the Webinar on Quark Matter and
Relativistic Hydrodynamics (Physics Department, Sharif University of
Technology, Tehran, Iran). The talk is followed by nearly an hour of
discussion with the audience (2020).

Strichartz
estimates for the compressible Euler equation with vorticity and
low-regularity solutions. Video of a talk I gave in the workshop Dynamics
in Geometric Dispersive Equations and the Effects of Trapping,
Scattering and Weak Turbulence that took place at the Banff
International Research Station in Banff, Canada (2020).

Here is a
Vanderbilt news story of a
Robert Noyce Scholarship grant (2019-2024) for which I am a
Co-Principal Investigator together with Principal Investigators
Heather Johnson and
Teresa Dunleavy, of the Department
of Teaching and Learning, and Co-Principal Investigators
David Weintraub of the Physics
Department, and
Isaac Thompson from Fisk
University (2019).

Here is a
news story with a short video description (in Portuguese) by the
Sociedade Brasileira de Fisica (Brazilian Physical Society)
describing my work Causality
of the Einstein-Israel-Stewart Theory with Bulk Viscosity (2019),
written with
Fabio S. Bemfica and Jorge
Noronha. Click here
to access the video directly (.mov file). The follow-up work, Nonlinear Constraints on Relativistic Fluids Far From Equilibrium (2021), that I wrote with
Fabio S. Bemfica, Vu Hoang, Jorge
Noronha, and Maria Radosz, was
also featured (in Portuguese) by the
Sociedade Brasileira de Fisica. (Click here
to access the video directly, .mov file.)

Here is a department
news story on the occasion of my 2018
Sloan Fellowship award. The announcement of the 2018 Sloan Fellows
also appeared in the
New York Times and in the American
Mathematical Society website. Here the Vanderbilt
news story (2018).

Here is a department
news story on the occasion of my 2019 Dean's
Faculty Fellowship award (2019).

The three-dimensional free
boundary Euler equations with surface tension. Video of a talk I
gave in the workshop Recent
Advances in Hydrodynamics that took place at the Banff
International Research Station in Banff, Canada (2016).

The "sticky" universe. A news story on a paper that I wrote with Robert Scherrer and Thomas Kephart. In 2015, the year the paper was published, it received widespread media coverage, including from The Guardian, Redorbit, New Statesman, The Huffington Post, among many others. This unexpected media attention led me to write some reflections on science and the media. In 2016, the paper was again in the news with stories in the Wired, BBC Brazil (in Portuguese), Revista Piauí (in Portuguese), and TV Cultura (in Portuguese). This story was in the cover of the 2017 department newsletter, Spectrum.

The "sticky" universe. A news story on a paper that I wrote with Robert Scherrer and Thomas Kephart. In 2015, the year the paper was published, it received widespread media coverage, including from The Guardian, Redorbit, New Statesman, The Huffington Post, among many others. This unexpected media attention led me to write some reflections on science and the media. In 2016, the paper was again in the news with stories in the Wired, BBC Brazil (in Portuguese), Revista Piauí (in Portuguese), and TV Cultura (in Portuguese). This story was in the cover of the 2017 department newsletter, Spectrum.

The Einstein system for
inviscid and viscid relativistic fluids (.flv file). Video of a
talk I presented at the Colloquium of the Department of
Applied Mathematics at USP, Brazil. The talk was in Ensligh,
although the introduction and Q&A were in Portuguese (2013).

I am occasionally a guest in the radio program Fronteiras
da Ciencia, a radio program (in Portuguese) dedicated to science
discussions for the general public. I participated in the episodes Gravitacao
quantica (2013), Teoria
de
supercordas (2013), A
grande ruptura cosmica (big rip) (2017), and a discussion
about the work of Stephen Hawking (2018) on the occasion of his
passing (mp3 files).

Other links and useful material

The
Comprehensive
LaTex symbol list - excellent material by Scott Pakin (pdf file).

Simons Center for Geometry and Physics - the intellectual focus of the Center is at the interface of Mathematics, in particular Geometry, and Theoretical Physics.

Simons Center for Geometry and Physics - the intellectual focus of the Center is at the interface of Mathematics, in particular Geometry, and Theoretical Physics.