epfl phd math

Study plans

Mathematics 2023-24

Core courses.

Chair of Mathematical Data Science

Institute of mathematics and school of computer and communication sciences, co-director of the bernoulli center for fundamental studies, senior research scientist at apple (aiml-mlr).

Publications
SwissCardIA

Deepfoundations

The Chair of Mathematical Data Science (MDS) focuses on mathematical principles and algorithms for data science and AI. As branches of mathematics, it mainly involves probability, statistics, discrete mathematics, and as more specific fields, machine learning and information theory.

Emmanuel Abbe received his Ph.D. degree from the EECS Department at the Massachusetts Institute of Technology (MIT) in 2008, and his M.S. degree from the Department of Mathematics at the Ecole Polytechnique FÃ©dÃ©rale de Lausanne (EPFL) in 2003. He was at Princeton University as an assistant professor from 2012-2016 and a tenured associate professor from 2016, jointly in the Program for Applied and Computational Mathematics and the Department of Electrical Engineering, as well an associate faculty in the Department of Mathematics at Princeton University since 2016. He joined EPFL in 2018 as a Full Professor, jointly in the Mathematics Institute and the School of Computer and Communication Sciences, where he holds the Chair of Mathematical Data Science.

He is the recipient/co-recipient of the Foundation Latsis International Prize; the Bell Labs Prize; the NSF CAREER Award; the Google Faculty Research Award; the Walter Curtis Johnson Prize from Princeton University; the von Neumann Fellowship from the Institute for Advanced Study; the IEEE Information Theory Society Paper Award; the Simons-NSF Mathematics of Deep Learning Collaborative Research Award; the ICML Outstanding Paper Award.

He is also a Global Expert at the Geneva Science and Diplomacy Anticipator (GESDA) , a member of the Steering Committee of the Center for Intelligent Systems (CIS) at EPFL , a member of the Deepfoundations collaboration on the theoretical foundations of deep learning, and the co-director of the Bernoulli Center for Fundamental Studies at EPFL. Emmanuel Abbe is also a senior research scientist at Apple MLR.

Selected publications

E. Boix-Adsera, O. Saremi, E. Abbe, S. Bengio, E.Littwin, J. Susskind, When can transformers reason with abstract symbols?, ICLR
S. d'Ascoli, S. Bengio, J. Susskind, E. Abbe, Boolformer: Symbolic Regression of Logic Functions with Transformers, .
E. Abbe, E. Cornacchia, A. Lotfi, Provable Advantage of Curriculum Learning on Parity Targets with Mixed Inputs, NeurIPS'23.
E. Boix-Adsera, E. Littwin, E. Abbe, S. Bengio, J. Susskind, Transformers learn through gradual rank increase, NeurIPS'23.
E. Abbe, C. Sandon, A proof that Reed-Muller codes achieve Shannon capacity on symmetric channels, FOCS'23. Invited to SICOMP Special Issue for FOCS
E. Abbe, S. Bengio, A. Lotfi, K. Rizk, Generalization on the Unseen, Logic Reasoning and Degree Curriculum, ICML'23 Oral. ICML Outstanding Paper Award
E. Abbe, E. Boix-Adsera, T. Misiakiewicz, SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics, NeurIPS’23
E. Abbe, S. Bengio, E. Cornacchia, J. Kleinberg, A. Lotfi, M. Raghu, C. Zhang, Learning to Reason with Neural Networks: Generalization, Unseen Data and Boolean Measures, NeurIPS’22
E. Abbe, E. Boix-Adsera, On the non-universality of deep learning: quantifying the cost of symmetry, NeurIPS’22
E. Abbe, E. Boix-Adsera, T. Misiakiewicz, The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networks, COLT’22
E. Abbe, E.Cornacchia, J. Hazla, C. Marquis, An initial alignment between neural network and target is needed for gradient descent to learn, ICML’22
E. Abbe, S. Li, A. Sly, Binary perceptron: efficient algorithms can find solutions in a rare well-connected cluster, STOC’21
E. Abbe, S. Li, A. Sly, Proof of the Contiguity Conjecture and Lognormal Limit for the Symmetric Perceptron, FOCS’21
E. Abbe, P. Kamath, E. Malach, C. Sandon, N. Srebro, On the power of differentiable learning versus PAC and SQ learning, NeurIPS’21 Spotlight
E. Abbe, E. Boix-Adsera, M. Brenner, G. Bresler, D. Nagarj, The staircase property: how hierarchical structure can guide deep learning, NeurIPS’21
E. Abbe, E. Cornacchia, Y. Gu, Y. Polyanskiy, Stochastic block model entropy and broadcasting on trees with survey COLT’21 Best Student Paper Award
E. Malach, P. Kamath, E. Abbe, N. Srebro, Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels , ICML’21
A. Asadi, E. Abbe, Maximum Multiscale Entropy and Neural Network Regularization
E. Abbe, J. Fan, K. Wang, An l_p theory of PCA and spectral clustering , Annals of Statistics
E. Abbe, S. Li, A. Sly, Learning sparse graphons and the generalized Kesten-Stigum Threshold , Annals of Statistics
E. Abbe, C. Sandon, Polytime universality and limitations of deep learning , CPAM
E. Abbe, A. Shpilka, M. Ye, Reed-Muller codes: theory and algorithms , Information Theory Trans.
E. Abbe, C. Sandon, On the universality of deep learning , NeurIPS 20
E. Abbe, M. Ye, Reed-Muller codes polarize. FOCS 19
Min Ye , Emmanuel Abbe , Recursive projection-aggregation decoding of Reed-Muller codes. ISIT 19
Amir R. Asadi , Emmanuel Abbe , Chaining Meets Chain Rule: Multilevel Entropic Regularization and Training of Neural Nets. JMLR
Emmanuel Abbe , Enric Boix-AdserÃ , Subadditivity Beyond Trees and the Chi-Squared Mutual Information. ISIT 19
E. Abbe, E. Boix, P. Ralli, C. Sandon, Graph powering and spectral robustness. SIAM Journal on Mathematics of Data Science
E. Abbe, E. Boix, An Information-Percolation Bound for Spin Synchronization on General Graphs . Annals of Applied Probability
A. Asadi, E. Abbe, S. Verdu Chaining mutual information and tightening generalization bounds . NIPS 18
E. Abbe, L. MassouliÃ©, A. Montanari, A. Sly, N. Srivastava, Group syncrhonization on grids . Mathematical Statistics and Learning (MSL) 18
M. Ye, E. Abbe, Communication-computation efficient gradient coding . ICML 18
A. Sankararaman, E. Abbe, F. Baccelli, Community Detection on Euclidean Random Graphs, Information and Inference: A Journal of the IMA
E. Abbe, T. Bandory, W. Leeb, J. Pereira, N. Sharon, A. Singer Multireference alignment is easier with an aperiodic translation distribution . Information Theory Trans.
E. Abbe, J. Fan, K. Wang, Y. Zhong, Entrywise eigenvector analysis of random matrices of low expected rank . Annals of Statistics
E. Abbe, S. Kulkarni, E. Lee, Generalized nonbacktracking bounds on the influence . JMLR
E. Abbe, Community detection and stochastic block models: recent development . JMLR
E. Abbe, S. Kulkarni, E. Lee, Nonbacktracking bounds on the influence in cascade models . NIPS 17
E. Abbe, J. Pereira, A. Singer, Sample complexity of the Boolean multireference alignment problem , ISIT 16
E. Abbe, C. Sandon, Proof of the achievability conjectures in the general stochastic block model . CPAM
E. Abbe, C. Sandon, Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap . NIPS 16 oral
E. Abbe, C. Sandon, Recovering communities in the general stochastic block model without knowing the parameters . NIPS 15
E. Abbe, C. Sandon, Community detection in the general stochastic block model: fundamental limits and efficient recovery algorithms update here . FOCS 15
E. Abbe, A. Shpilka, A. Wigderson, Reed-Muller codes for random erasures and erros . STOC 15
Y. Desphande, E. Abbe, A. Montanari, Asymptotic mutual information for the balanced binary SBM . Journal Information and Inference: A Journal of the IMA
E. Abbe, Y. Wigderson, High-girth matrices and polarization . ISIT 15
E. Abbe, A. Bandeira, G. Hall, Exact recovery in the stochastic block model . Information Theory Trans. IEEE Information Theory Society Best Paper Award
E. Abbe, N. Alon, A. Bandeira, Linear Boolean classification, coding and “the critical problem” . ISIT 14
E. Abbe, A. Bandeira, A. Bracher, A. Singer, Decoding graph labels from censored correlations: phase transition and efficient recovery . Transactions on Network Science and Eng.
E. Abbe, A. Montanari, Conditional random fields, planted constraint satisfaction and entropy concentration . Journal Theory of Computing
E. Abbe, A. Montanari, On the concentration of the number of solutions of random satisfiability formulas . Random Structures and Algorithms
N. Goela, E. Abbe, M. Gastpar, Polar codes for broadcast channels http://arxiv.org/abs/1301.6150 . Information Theory Trans.
E. Abbe, A. Khandani, A. W. Lo, Privacy-preserving methods in systemic risk . American Economical Review (AER) . New York Times article: http://bits.blogs.nytimes.com/2013/09/09/a-data-weapon-to-avoid-the-next-financial-crisis/

Theses & Reports

E. M. Chayti, Capacity of Binary perceptrons with binary inputs , MDS, Semester Project, 2020
E. Boix, Average-case statistical query algorithms , MDS, Summer internship report, 2019. Last version
E. Bamas, Learning Monomials , MDS, Semester projects report, 2018

Teaching at EPFL

Probabilities and statistics.

Revision of basic set theory and combinatorics.

Elementary probability: random experiment; probability space; conditional probability; independence.

Combinatorial statistics

Inference on graphs, post-docs & research staff, raphaã«l jean berthier, dorina thanou, phd students, elisabetta cornacchia, ortal yona senouf.

Elena Grigorescu

SwisscardIA

The EPFL Chapter of the Society for Industrial and Applied Mathematics

Online seminar on optimal sampling

This Wednesday (April 17th), we are pleased to host a talk by Philippe Trunschke (PostDoc at Centrale Nantes & Nantes Université), which should be interesting to many of our members!

The seminar will take place online at the zoom link below, and will also be projected live in the room CM 1 517. https://epfl.zoom.us/j/61353461236?pwd=MnI2VkRMWlE2WUJxalRmNVJwc2JGQT09

Title: Optimal sampling for stochastic gradient descent

Abstract: Approximating high-dimensional functions often requires optimising a loss functional that can be represented as an expected value. When computing this expectation is unfeasible, a common approach is to replace the exact loss with a Monte Carlo estimate before employing a standard gradient descent scheme. This results in the well-known stochastic gradient descent method. However, using an estimated loss instead of the true loss can result in a “generalisation error”. Rigorous bounds for this error usually require strong compactness and Lipschitz continuity assumptions while providing a very slow decay with increasing sample size. This slow decay is unfavourable in settings where high accuracy is required or sample creation is costly. To address this issue, we propose a new approach that involves empirically (quasi-)projecting the gradient of the true loss onto local linearisations of the model class through an optimal weighted least squares method. The resulting optimisation scheme converges almost surely to a stationary point of the true loss, and we investigate its convergence rate.

Philipp TRUNSCHKE studied Mathematics at the Humboldt University in Berlin, specialising in statistical learning theory. He completed his doctoral studies focusing on tensor product approximation at the Technical University of Berlin 2018. Currently, he is working with Anthony NOUY in Nantes on compositional function networks and optimal sampling.

EPFL students @ SIAM UQ24 (Uncertainty Quantification)

Several EPFL PhD students, and members of the SIAM student chapter, were in Trieste last week for the SIAM conference on Uncertainty Quantification ! You can read about some of them in this LinkedIn post by CSQI lab (of EPFL’s math department).

PhD prize in Quantitative Research by G-Research

The company G-Research is organizing a PhD prize in Quantitative research of up to € 5,000! Open to final or penultimate PhD years at EPFL, working across areas including, but not limited to: Machine Learning, Quantitative Finance, Mathematics, Computer Science.

See the poster below for application details, or this EPFL webpage . The deadline for applications is March 28th, 2024. Important: Please note that doctoral candidates must have the permission of their thesis director(s) to apply for the prize in order to be able to share thesis data with a private company!

Seminar on AlphaTensor – Francisco Ruiz (Google DeepMind)

We were honored to host Francisco Ruiz, Research Scientist @ Google DeepMind, for an online seminar on AlphaTensor, last Tuesday 05/12 evening.

AlphaTensor is a Deep Reinforcement Learning agent designed to automatically discover fast algorithms for matrix multiplication, a mathematical operation ubiquitous in science and engineering. It discovered new improved algorithms, with heavy impact on theory and practice. Francisco spoke about its development and shared firsthand insights into its design. Memento link

SIAM Career Event

We were delighted to host Matthew Wiener, Justina Ivanauskaite and Radu Popescu for a Career Event, last Monday 04/12 evening. They presented their experience working in Applied Math, Computational Science or Data Science in different industries (from pharmaceutical to supply chain management to high-performance computing…), making these career paths more concrete to Master and PhD students in those fields. The event was followed by a networking apéro. Memento link

Fête des maths @ EPFL

Very happy to have had so many people come by our booth at the Fête des maths @ EPFL last Saturday (Nov 25th)! Members of the student chapter presented some of their numerical experiments, from fluid models of plasma, to thermal cloaking solutions, to simulation of blood flow in a carotid artery. Visitors of all ages and backgrounds stopped by, including an unexpected celebrity visit, Maryna Viazovska!

G-Research Quant Finance Workshop 2023 (2)

Thanks to all the participants to the G-research Quant Finance Workshop on 11th October, as well as to the people from G-Research, and congratulations to the two winning teams! We hope to see you again at the next event — to be announced, stay tuned!

G-Research Quant Finance Workshop 2023

We are pleased to invite you to join the 2023 edition of the G-Research Quant Finance workshop @ EPFL! It will take place on Wednesday 11th October starting from 6pm , in GC C3 30 . As last year, it will consist of a Python-based challenge in teams of three, networking with people from G-Research, and food and beverages. Sign up here: https://qrco.de/EPFLQuantChallenge23

We are happy to relay the announcement of the program Scimpact organized by Reatch, which may be of interest to some students at EPFL:

You want to learn how to write a good blog-article or moderate a discussion? You want to be part of a young science community that wants to make a difference? Welcome to Scimpact! Scimpact is a training program for young people who want to bring science into societal debates. The program consists of hands-on workshops and 1:1 coaching, lasts 4 or 8 months and offers you the chance to organize a public event! Apply by September 30 at www.reatch.ch/en/scimpact

G-Research Quant Finance Challenge

On Thursday 3rd November 2022, G-Research came to the EPFL campus for a “Quant Finance Challenge” , an algorithmic trading-based game. In teams of 2-3, over 100 Master, PhD students and postdocs tried their hands (and their Python skills) at a few problems inspired from quantitative finance.

The Challenge was followed by pizza and drinks, and the opportunity to discuss with Quant Researchers and Machine Learning Specialists from G-Research.

Martin Licht

Bernoulli instructor at epfl, switzerland.

[email protected]

Google Scholar

Lausanne, Switzerland

Martin Licht EPFL SB MATH MATH-GE Station 8 CH-1015 Switzerland

I am a postdoctoral researcher at the Department of Mathematics at EPFL, Switzerland. My research focuses finite element methods for partial differential equations in electromagnetism, elasticity, and relativity.

After my PhD at the University of Oslo, I was a visiting assistant professor at UCSD. I have been visitor at the University of Minnesota, Cambridge University, and Brown University.

In my free time, I paint with acrylics and learn Mandarin.

Positions & Activities

Publications.

Complexes of discrete distributional differential forms and their homology theory, Found Comput Math (2017) 17: 1085-1122. [Arxiv] [Journal] --> [Journal]
Smoothed projections over weakly Lipschitz domains. Math. Comp. 88 (315), 179-210 [Arxiv] [Download] [Journal] --> [Journal]
Smoothed projections and mixed boundary conditions. Math. Comp. 88 (316), 607-635 [Arxiv] [Download] [Journal] --> [Journal]
Poincaré-Friedrichs inequalities for complexes of distributional differential forms. With Snorre Christiansen. Bit Numer Math 60, 345-371. [Download] [Journal] --> [Journal]
A divergence-conforming finite element method for the surface Stokes equation. With Andrea Bonito and Alan Demlow. SIAM J. Numer. Anal. 58(5), 2764-2798. [Arxiv] [Journal] --> [Journal]
Local finite element approximation of Sobolev differential forms. With Michael Holst and Evan Gawlik. ESAIM: M2AN 55(5), 2075-2099. [Arxiv] [Journal] --> [Journal]
On basis constructions in finite element exterior calculus. Adv Comput Math 48, 14 (2022). [Arxiv] [Download] [Journal]
Symmetry and invariant bases in finite element exterior calculus. Found Comput Math. (2023) [Arxiv] [Journal] [Download] --> [Journal] --> [Download] -->
Geometric transformation of finite element methods: theory and applications. With Michael Holst. Applied Numerical Mathematics 192, 389-413 [Arxiv] [journal]
Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Orlicz-Sobolev-Slobodeckij and bounded variation spaces. Journal of Mathematical Analysis and Applications 534 (1) [Arxiv] [Journal]
On Lipschitz partitions of unity and the Assouad–Nagata dimension Topology and its Applications 348. [Arxiv] [Journal]
Smoothed projections over manifolds in finite element exterior calculus. Submitted. [Arxiv]
Towards finite element exterior calculus over manifolds: commuting projections, geometric variational crimes, and approximation errors. Conference Proceedings ENUMATH 2023. Submitted. [Arxiv]
Averaging-based local projections in finite element exterior calculus. Submitted. [Arxiv]
Constructing collars in paracompact spaces and Lipschitz estimates in metric spaces Submitted. [Arxiv]
Newest Vertex Bisection over general triangulations. With Michael Holst and Zhao Lyu. Submitted. [Download] [Arxiv] -->
Higher-Order finite element de Rham complexes, partially localized flux reconstructions, and applications. Submitted. [Download]
Finite Element Methods for Linear Maxwell's Equations in Bianisotropic Media Permitting Polarization Fields and Magnetic Currents. Submitted. [Arxiv]
Computable reliable bounds for Poincaré–Friedrichs constants via Čech–de-Rham complexes. Special Issue of Results in Applied Mathematics. In Preparation.
Mixed Surface Finite Element Approximation for the Stationary Darcy Flow. With Alan Demlow and Andrea Bonito. In Preparation. [Download] [Arxiv]

Theses and Reports

On the A Priori and A Posteriori Error Analysis in Finite Element Exterior Calculus. PhD thesis in mathematics, Oslo, 2017. [Download]
Smoothed Analysis of Linear Programming. Diplom thesis in computer science, Bonn, 2013. [Download]
Diskrete distributionelle Differentialformen und ihre Anwendungen. Diplom thesis in mathematics, Bonn, 2012.
Domain Distribution for parallel Modeling of Root Water Uptake. Proceedings 2010, JSC Guest Student Programme on Scientific Computing, 2010. [Link to proceedings]

Research Interests

Finite element methods, Finite element exterior calculus
Structure-preserving numerical methods for partial differential equations
Partial differential equations over manifolds, geometric analysis
Numerical linear algebra
Algorithms and approximation theory of artificial neural networks

Why do we need edge elements?

Edge elements are necessary for physically correct finite element approximations in numerical electromagnetism. This inevitable leads to the use of mixed finite element methods. By contrast, finite element methods that naively use Lagrange elements for the coordinates and minimize energy functionals stably converge to incorrect solutions. This is catastrophic because the inconsistency may not be apparent to every user of finite element methods.

The finite element solution using edge elements correctly resolves the corner singularity of the problem. The plot depicts the vector field variable and the magnitude of the solution. As the mesh is refined, the finite element approximation converges to the physically correct solution.

A boilerplate finite element method, simply using Lagrange elements for each coordinate, converges to an incorrect solution as the mesh is refined. While this vector field may look permissible to the untrained eye, it is qualitatively different from the correct solution.

Discrete harmonic vector fields

Discrete harmonic vector fields on a square subject to mixed boundary conditions: we impose tangential boundary conditions along the middle parts of the four boundary faces and normal boundary conditions near the corners. Even though the domain is simply connected, the space of harmonic vector fields is non-trivial. Its dimension is the first relative Betti number of the domain, which equals 3 in this example. The low elliptic regularity of the vector Laplace equation in the presence of mixed boundary conditions is apparent.

Discrete harmonic vector fields on an anulus, computed with a lowest-order Nedéléc method. Once with tangential boundary condition (left), then with normal boundary conditions (right). The space of harmonic vector fields reflects the non-trivial topology of the domain.

Complexity of adaptive mesh refinement

Triangulations of an approximate sphere. My research has led to the first completely combinatorial amortized complexity estimate for repeated newest vertex bisection. Newest vertex bisection is a key component in the mesh refinement algorithm of adaptive finite element methods. Previous complexity estimates involved geometric quantities that lead to suboptimal estimates when the initial mesh is highly non-uniform.

Structure-Preserving Numerical Methods for Partial Differential Equations

Bernoulli center, lausanne, switzerland, july 3-7, 2023, https://suprenumpde2023.epfl.ch/.

- Douglas Arnold
- Ralf Hiptmair
- Snorre Christiansen
- Annalisa Buffa
- Joachim Schöberl

Selected Presentations

Joint Mathematics Meeting 2024, San Francisco. January 3-6, 2024. Talk: Computable reliable bounds for Poincaré–Friedrichs constants via Čech–de-Rham complexes
ENUMATH 2023, Lisbon, Portugal. September 4-8, 2023. Talk: The broken Bramble-Hilbert lemma for differential forms and its applications
Swiss Numerics Day, University of Bern. June 7, 2023. Talk: Towards finite element exterior calculus on manifolds.
30th Birthday of Acta Numerica, Banach Centre at Bedlewo. June 26-July 2, 2022. Talk: Averaging-based local projections in finite element exterior calculus.
Oberwolfach Workshop Hilbert Complexes: Analysis, Applications, and Discretizations, Oberwolfach Center. June 19-25, 2022.
HCM Workshop Synergies between Data Science and PDE Analysis, HCM Bonn. June 13-17, 2022.
Hausdorff School Foundational Methods in Machine Learning, HCM Bonn. June 6-10, 2022.
Zurich Colloquium in Applied and Computational Mathematics, ETHZ. April 6, 2022.
Conference on Fast Direct Solvers, Purdue University. October 23-24, 2021.
Swiss Numerics Day 2021, EPFL, Switzerland. September 13, 2021. Talk: Local finite element approximation of Sobolev differential forms.
11th Zurich Summer School 2021: Asymptotic Methods in Physical and Numerical Modelling. University of Zurich, Switzerland. August 23-27, 2021. Poster: Local finite element approximation of Sobolev differential forms.
Spring 2021 Finite Element Circus (online). University of Delaware. April 9-10, 2021. Talk: Local finite element approximation of Sobolev differential forms.
Center for Computational Mathematics Seminar (Virtual). UC San Diego. December 8, 2020. Talk: De Rham Regularizers and Compatible Discretizations
Workshop Statistical Methods for the Detection, Classification, and Inference of Relativistic Objects (Virtual). ICERM, Providence, RI. November 16–20, 2020.
Workshop Mathematical and Computational Approaches for the Einstein Field Equations with Matter Fields (Virtual). ICERM, Providence, RI. October 26–30, 2020.
Workshop Mathematical and Computational Approaches for Solving the Source-Free Einstein Field Equations (Virtual). ICERM, Providence, RI. October 5–9, 2020.
Workshop Advances and Challenges in Computational Relativity (Virtual). ICERM, Providence, RI. September 14–18, 2020.
Math Postdoc Seminar, UC San Diego, February 5, 2020. Talk: An Introduction to the Mathematics of Artificial Neural Networks.
Workshop Applications of Geometric and Structure Preserving Methods. Isaac Newton Institute, Cambridge, UK. December 3, 2019.
Mathematical Seminar University of Nottingham, UK. November 6, 2019. Talk: A divergence-conforming finite element method for the surface Stokes equation.
Simons Wave Collaboration Workshop Spectral Computations In Quantum Mechanics and Applications to Material Structure. Maxwell Centre, Cambridge, UK. October 23–24, 2019. Poster: Newest Results in Newest Vertex Bisection.
Conference The Future of Structure-Preserving Algorithms. Bayes Centre, Edinburgh, UK. October 14–18, 2019. Talk: Experiences implementing finite element differential forms in C++.
Seminar Geometry, compatibility and structure preservation in computational differential equations. Isaac Newton Institute, Cambridge, UK. September 25, 2019. Talk: Newest Results in Newest Vertex Bisection.
ICIAM 2019 meeting. Valencia, Spain. July 15–19, 2019. Talk: On the Basis construction in finite element exterior calculus.
Tutorial Workshop Geometry, compatibility and structure preservation in computational differential equations. Isaac Newton Institute, Cambridge, UK. July 8–12, 2019.
MAFELAP 2019. Brunel University, United Kingdom. June 17–21, 2019. Talk: Finite element methods for the Curl-Curl equation with mixed boundary conditions.
AMS Spring Central and Western Joint Sectional Meeting. University of Hawaii at Manoa, Honolulu, HI. March 22–24, 2019. Co-organized workshop. Talk: Newest Results in Newest Vertex Bisection.
SIAM GS19. Houston, TX. March 11–14, 2019. Talk: On the Basis construction in finite element exterior calculus.
Computational Mathematics Seminar. UC San Diego. February 26, 2019. Talk: Newest Results on Newest Vertex Bisection.
Computational Mathematics Seminar. UC San Diego. October 16, 2018. Talk: On Basis Constructions in Finite Element Exterior Calculus.
SIAM TX-LA Sectional Meeting. Louisiana State University. October 5–7, 2018. Talk: On the Basis construction in finite element exterior calculus.
SIAM Annual Meeting. Oregon Convention Center, Portland, OR. July 9–13, 2018. Talk: Intrinsic finite element methods over manifolds.
Computational Mathematics Seminar. UC San Diego. January 30, 2018. Talk: A New Approach to FEM for Non-Polygonal Domains.
Workshop: GR + FEEC @ UCSD. UC San Diego. January 13–16, 2018. Talk: Smooth commuting projections in rough settings: Weakly Lipschitz domains and mixed boundary conditions.
Joint Mathematics Meeting. UC San Diego. January 12, 2018. Talk: Intrinsic finite element methods over manifolds.
Computational Mathematics Seminar. UC San Diego. October 24, 2017. Talk: Smooth commuting projections in rough settings: Weakly Lipschitz domains and mixed boundary conditions.
Computational Mathematics Seminar. Texas A&M University. September 20, 2017. Talk: Smooth commuting projections in rough settings: Weakly Lipschitz domains and mixed boundary conditions.
Structure and Scaling in Computational Field Theories. ESC Workshop. University of Oslo, Norway, October 9–13, 2016. Talk: Smoothed Projections over Manifolds.
New Trends in Compatible Discretizations. CEA-EDF-Inria School. INRIA Paris-Rocquencourt, France, June 29–July 2, 2015. Poster: Discrete distributional differential forms.
Structure-Preserving Discretizations of Partial Differential Equations. University of Minnesota, Minneapolis, USA, October 22–25, 2014. Poster and Talk: Discrete distributional differential forms.

Undergraduate Supervision

Jiyue Zeng recently received the prestigious 2020 Physical Sciences Dean’s Undergraduate Award for Excellence . I supervise her on a project in optimization methods with applications to numerical analysis of partial differential equations.
Tharindu Fernando is currently a graduate student of physics at the University of Washington. I supervised his undergraduate research on different formulations of Maxwell's equations and finite element implementations.
Xinyi He is an undergraduate student of mathematics and computer science at UC San Diego. She is admitted to UCSD's highly selective Bachelor-Master's programme in Computer Science. We collaborate on asynchronous iterative methods in numerical linear algebra.
Zhao Lyu received the prestigious 2018 Physical Sciences Dean’s Undergraduate Award for Excellence . I supervised her undergraduate thesis on algorithms for adaptive mesh refinement. She completed her master's degree in Computational Science and Engineering at Harvard University. She is currently a PhD student in Computational and Applied Mathematics at the University of Chicago.
Tâm Johan Nguyen is a Master student at EPFL. I supervised his project on computing Betti curves in persistent homology.
Analysis IV (for Electrical Engineering, Mechanical Engineering, and Material Sciences) — EPFL, Math-207(c), Spring Semester 2024
Numerical Methods for Conservation Laws — EPFL, Math-459, Winter Semester 2023
Analysis III (for Electrical Engineering, Mechanical Engineering, and Material Sciences) — EPFL, Math-202(c), Winter Semester 2023
Numerical Approximation for Partial Differential Equations, Math-451, Summer Semester 2022
Numerical Methods for Conservation Laws — EPFL, Math-459, Winter Semester 2022
Analysis IV (for Life Sciences and Microtechnology) — EPFL, Math-207, Summer Semester 2022
Numerical Methods for Conservation Laws — EPFL, Math-459, Winter Semester 2021
Numerical Methods for Partial Differential Equations — UCSD, Math 175/275, Spring Quarter 2021
Numerical Methods for Physical Modeling — UCSD, Math 174/274, Winter Quarter 2021
Calculus for Science and Engineering II — UCSD, Math 20B, Winter Quarter 2021
Introduction to Numerical Analysis: Ordinary Differential Equations — UCSD, Math 170C, Spring Quarter 2020
Linear Algebra — UCSD, Math 18, Spring Quarter 2020, Math 18
Introduction to Numerical Analysis: Approximation and Nonlinear Equations — UCSD, Math 170B, Winter Quarter 2020
Linear Algebra — UCSD, Math 18, Winter Quarter 2020
Mathematical Reasoning — UCSD, Math 109, Spring Quarter 2019
Introduction to Numerical Analysis: Linear Algebra — UCSD, Math 170A, Winter Quarter 2019
Introduction to Numerical Analysis: Approximation and Nonlinear Equations — UCSD, Math 170B, Winter Quarter 2019
Numerical Linear Algebra — UCSD, Math 270A, Fall Quarter 2018
Calculus III — UCSD, Math 10C, Spring Quarter 2018
Mathematical Reasoning — UCSD, Math 109, Winter Quarter 2018
Applied Linear Algebra — UCSD, Math 102, Fall Quarter 2017

Miscellaneous recommendations

Restaurant Recommendations in Cambridge (and beyond)
Travel preparation and checklist
Several tricks for SSH on Github
Using Clang++ and Make natively on Windows
Profiling C++ on Linux
SciPosterHTML: scientific conference posters in HTML, CSS, and MathJax A collection of examples for scientific conference posters in HTML and CSS. Lightweight, ready to go and easy to modify for your purposes.
C implementation of Karatsuba-Ofman algorithm for big integer multiplication Winning contribution to the 2007 Bonn C Programming Competition, now archived on Github.
Check whether your project files are compliant to common file systems
What is your fastest C integer type on your machine?
Global Routing (soon to come) Global Routing (soon to be come) -->

Postal address: EPFL SB MATH MATH-GE Station 8 CH-1015 Switzerland

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Online People Directory

Maryna viazovska.

[email protected] +41 21 693 00 33 https://www.epfl.ch/labs/tn/

EPFL SB MATH TN MA B3 444 (Bâtiment MA) Station 8 1015 Lausanne

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Web site: Web site: https://sma.epfl.ch/

EPFL CIB GA 3 34 (Bâtiment GA) Station 5 1015 Lausanne

+41 21 693 00 33 Office: GA 3 34 EPFL > VPA-AVP-CP > CIB > CIB-GE

Web site: Web site: https://bernoulli.epfl.ch

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Publications

Selected publications, teaching & phd.

Mathematics

Past EPFL PhD Students

Discrete mathematics, number theory ii.a - modular forms, all postal addresses and positions.

EPFL SB MATH TN Full Professor Status: Staff

EPFL SB SB-SMA SMA-ENS Full Professor Status: Staff

EPFL VPA-AVP-CP CIB CIB-GE Executive committee member Status: Staff

Past Programs

Young Researchers in Mathematics Program

The Bernoulli Center for Fundamental Studies is a world-renowned research institute located in Lausanne, Switzerland, facilitating research, outreach, and education in mathematics and the mathematical sciences. The Young Researchers in Mathematics Program is a new and exciting summer research program hosted by the Bernoulli Center, offering a unique opportunity for students in mathematics to gain valuable research experience during the summer of 2022.

The purpose of the program is to bring together a cohort of talented students from around the world to engage in an immersive research experience. Participants in the program will work closely with one another to develop a joint research project fit for publication.

Who can apply:

The program is aimed for students who

are not yet in a PhD program but show interest in pursuing a PhD in mathematics. (Students who have already been accepted into a PhD program, including those who are scheduled to start their PhD in Fall 2022, are not eligible to apply.)
are eager to develop a collaborative research project with other budding mathematicians and want to learn more about producing and publishing research in mathematics.
are interested in NUMBER THEORY (which will be the main topic of the proposed research project this summer).

Structure of the program

The program has both online and in-person components and is structured as follows:

Phase 1 – Online Reading: Participants will receive reading material to bring everyone up to speed on the topic of the research project.

Phase 2 – In-Person Collaboration: This is the main event of the program. It consists of a one-week in-person collaboration at the Bernoulli Center where the actual work on the project begins. This week also includes social activities (such as dinner&drinks, sightseeing, outdoor activities, etc.).

Phase 3 – Online Collaboration: After the intensive one-week in-person component, the collaboration continues online via weekly zoom meetings to finish the research project.

When and Where:

The in-person component of the program will take place from July 11 to July 17, 2022, at the Bernoulli Center for Fundamental Studies, which is located on campus of the École Polytechnique Fédérale de Lausanne (EPFL). Students accepted to the program have their travel and on-site expenses fully covered by the Bernoulli Center (including international travel). Housing and assistance with making travel arrangements will be provided.

How to apply:

The application is over for 2022 but please, connect again with us in spring 2023 to apply for next summer program.

Start date & time

End date & time

Bernoulli Center (Lausanne)

Bernoulli Center

Prof. Florian Richter

Christiane Maillard & Eliane Rasch
EPFL AVP-CP CIB
GA 3 34 (Bâtiment GA), Station 5 CH-1015 Lausanne
+41 21 693 64 30
[email protected]
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Bernoulli Center for Fundamental Studies

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Doctoral students in Mathematics Education and Teacher Education and Teacher Development present at national conference

Posted in: Research Presentations

John O'Meara and Shanna Anderson at NARST conference

John O’Meara, PhD student in Mathematics Education, presented a paper with Shanna Anderson, PhD student in Teacher Education and Teacher Development (TETD), at the National Association of Research in Science Teaching (NARST) conference in Denver, CO on March 19, 2024. They presented their work on Social Network Maps: Supporting STEM Teacher Leaders and Characterizing the Phenomenon of Teacher Leadership, funded by the Wipro Science Education Fellowship grant.

They represented their research team, which includes Drs. Mika Munakata , Emily Klein and Monica Taylor (College of Education and Engaged Learning) and Tim Aberle (PhD student in TETD). Congratulations, all!

The PhD Council Podcast dives into the world of PhD life at TU Delft's Electrical Engineering, Mathematics and Computer Science Faculty (EEMCS). We cover research, challenges, and practical tips. We interview PhDs, professors, and postdocs to share their experiences and insights, helping fellow PhD candidates navigate their academic journey effectively. Join us for candid discussions and valuable advice to make the most of your doctoral studies.

PhD Life by PhD Council PhD Council

APR 17, 2024

PhD Deep Dive: Youri Blom

The sixth episode in our series, in which we dive deep into topics that PhDs in our faculty are working on. Youri's PhD is on Photovoltaic Materials and Devices in the department of Electrical Sustainable Energy. The group specializes in applying advanced measurement techniques in combination with computer modeling for determination of (opto-) electronic properties, such as the density of defects in thin layers of disordered materials. The acquired expertise is used for the optimiz...

PhD Deep Dive: Willem de Muinck Keizer

The fourth episode in our series, in which we dive deep into topics that PhDs in our faculty are working on. Willem de Muinck Keizer is a PhD student at the Discrete Mathematics and Optimization group at the TU Delft. He works in semidefinite programming, which is a type of optimization problem with applications in and outside of Mathematics.

PhD Deep Dive: Lorena Poenaru-Olaru

The third episode in our series, in which we dive deep into topics that PhDs in our faculty are working on. Lorena's goal is to create a systematic method of monitoring and maintaining machine learning models in production against concept drift (data shifts). As part of the AI4FinTech Lab, I am enhancing the collaboration between academia (TU Delft) and industry (ING).

PhD Deep Dive: Ids van der Werf

The second episode in our series, in which we dive deep into topics that PhDs in our faculty are working on. Starting in August 2022, Ids is a PhD student at SPS with Richard Hendriks, working on a project about underwater communications, more specifically about creating a high bandwidth, doppler tolerant communication link. The project is a collaboration between TNO (a dutch research institute), the NLDA (Dutch defence academy) and the TU Delft.

PhD Deep Dive: Carolina Centeio Jorge

First episode in our series, in which we dive deep into topics that PhDs in our faculty are working on. Since October 2020, Carolina is a PhD student at the Interactive Intelligence group of TU Delft. Her PhD has a special focus on mental models in the context of human‐AI teams, such as enabling artificial agents (e.g., robots) to understand and predict human teammates and effectively act accordingly. Carolina's main research interests lie in Behaviour Analysis and Pattern Recognition.

Top Podcasts In Education

An AI leap into chemical synthesis

EPFL scientists introduce ChemCrow, a large language model-based AI system that revolutionizes chemistry by integrating 18 advanced tools for tasks like organic synthesis and drug discovery. ChemCrow streamlines complex processes in chemical research, making it more efficient for experts and novices alike.

Chemistry, with its intricate processes and vast potential for innovation, has always been a challenge for automation. Traditional computational tools, despite their advanced capabilities, often remain underutilized due to their complexity and the specialized knowledge required to operate them.

Now, researchers with the group of Philippe Schwaller at EPFL, have developed ChemCrow, an AI that integrates 18 expertly designed tools, enabling it to navigate and perform tasks within chemical research with unprecedented efficiency. "You might wonder why a crow?" asks Schwaller. "Because crows are known to use tools well."

ChemCrow was developed by PhD students Andres Bran and Oliver Schilter (EPFL, NCCR Catalysis) in collaboration with Sam Cox and Professor Andrew White at (FutureHouse and University of Rochester).

ChemCrow is based on a large language model (LLMs), such as GPT-4, enhanced by LangChain for tool integration, to autonomously perform chemical synthesis tasks. The scientists augmented the language model with a suite of specialized software tools already used in chemistry, including WebSearch for internet-based information retrieval, LitSearch for scientific literature extraction, and various molecular and reaction tools for chemical analysis.

By integrating ChemCrow with these tools, the researchers enabled it to autonomously plan and execute chemical syntheses, such as creating an insect repellent and various organocatalysts, and even assist in discovering new chromophores, substances fundamental to dye and pigment industries.

What sets ChemCrow apart is its ability to adapt and apply a structured reasoning process to chemical tasks. "The system is analogous to a human expert with access to a calculator and databases that not only improve the expert's efficiency, but also make them more factual -- in the case of ChemCrow, reducing hallucinations," explains Andres Camilo Marulanda Bran, the study's first author.

ChemCrow receives a prompt from the user, plans ahead how to solve the task, selects the relevant tools, and iteratively refines its strategy based on the outcome(s) of each step. This methodical approach ensures that ChemCrow doesn't only work off theory but is also grounded in practical application for real-world interaction with laboratory environments.

By democratizing access to complex chemical knowledge and processes, ChemCrow lowers the barrier to entry for non-experts while augmenting the toolkit available to veteran chemists. This can accelerate research and development in pharmaceuticals, materials science, and beyond, making the process more efficient and safer.

The group of Philippe Schwaller is part of the new EPFL AI Center , with more than forty other laboratories, leading the way towards trustworthy, accessible and inclusive AI.

Organic Chemistry
Inorganic Chemistry
Biochemistry
Computer Modeling
Mathematical Modeling
Organic chemistry
Global climate model
Mathematical model
Artificial neural network
Computer simulation
Resonance (chemistry)

Story Source:

Materials provided by Ecole Polytechnique Fédérale de Lausanne . Original written by Nik Papageorgiou. The original text of this story is licensed under Creative Commons CC BY-SA 4.0 . Note: Content may be edited for style and length.

Journal Reference :

Andres M. Bran, Sam Cox, Oliver Schilter, Carlo Baldassari, Andrew D. White, Philippe Schwaller. Augmenting large language models with chemistry tools . Nature Machine Intelligence , 2024; DOI: 10.1038/s42256-024-00832-8

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