Marius Lemm

Mathematical exploration and discovery at scale AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines ...

A new paper with Bogdan Georgiev, Javier Gomez-Serrano, and Adam Zsolt Wagner: "Mathematical exploration and discovery at scale" arxiv.org/abs/2511.02864. Further discussion is at terrytao.wordpress.com/2025/11/05/m...

Are the dynamics of disordered quantum many-body systems easier to simulate?

--> Yes, because entanglement spreads slowly for a non-perturbatively long time (a.k.a. "prethermal MBL"). This is true in any dimension.

arxiv.org/pdf/2510.11831

Thanks to my collaborators Ben McDonough and Andy Lucas!

A Formalization of the Generalized Quantum Stein's Lemma in Lean The Generalized Quantum Stein's Lemma is a theorem in quantum hypothesis testing that provides an operational meaning to the relative entropy within the context of quantum resource theories. Its origi...

The future is here: a formalization in Lean of the generalized quantum Stein's lemma!
Amazing that this can be done.
arxiv.org/abs/2510.08672

Learning Coulomb Potentials and Beyond with Fermions in Continuous Space We present a modular algorithm for learning external potentials in continuous-space free-fermion models including Coulomb potentials in any dimension. Compared to the lattice-based approaches, the con...

New preprint on Hamiltonian Learning of Coulomb potentials and smooth potentials in continuous space

arxiv.org/abs/2510.08471

Thanks to my collaborators, @hippoquantus.bsky.social , Tim Möbus, and Oliver Siebert!

New preprint with @nickrhj.bsky.social

arxiv.org/pdf/2509.22438

Is a typical translation-invariant Hamiltonian gapped or gapless?

---> We prove that for random rank-1 interactions on any bounded-degree graph, the Hamiltonian is *gapped* with high probability as local dimension grows.

Horng-Tzer Yau has spent decades studying the interplay of randomness and order in matrices. In 2008, Jun Yin, a former physicist, joined Yau’s group. In spring of 2024, the pair made the biggest advance on the problem since the 1980s.
www.quantamagazine.org/new-physics-...

Open position in Tübingen!

Assistant Professor of Mathematical Quantum Theory
(non tenure-track, up to 6 years)

Deadline is September 30, 2025.

More info including how to apply: www.mathjobs.org/jobs/list/26...

The last person to hold this position was the formidable @angelacapel.bsky.social

Understanding Quantum Information and Computation This is a course on the theory of quantum computing. It consists of 16 lessons, each with a video and written component, covering the basics of quantum information, quantum algorithms (including query...

After 3 1/2 years of work my course on quantum computing is finally finished — the "Director's Cut" of Understanding Quantum Information and Computation is now available.

arxiv.org/abs/2507.11536

Colored droplets in corn syrup seemingly blended together can be returned to their original state by reversing the direction of mixing, a form of laminar flow called "Stokes flow".

Credit: UNM Physics & Astronomy

How a Puzzle About Fractions Got Brain Scans Rolling (Gift Article) A story of bowling pins, patterns and medical miracles.

My latest for @nytimes.com -- please repost so your followers can see this for free. www.nytimes.com/interactive/...

2. DPG-Herbsttagung: 100 Jahre Quantenmechanik

This year, the fall meeting of the German Physical Society celebrates 100 years of quantum theory

quantum25.dpg-tagungen.de
Göttingen, September 8-12

The deadline for abstract submission is this Saturday, May 31.

On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all momen...

New preprint with Carla Rubiliani and Jingxuan Zhang

"On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians"

arxiv.org/abs/2505.01786

We prove that the speed of boson propagation is bounded under the optimal long-range condition (for power law exponent \alpha>d+1)

YouTube video by 3Blue1Brown But what is quantum computing? (Grover's Algorithm)

Great explanation of the basics of quantum computing and Grover's algorithm by 3Blue1Brown. He also addresses the common misconception of "exponential parallelism".
www.youtube.com/watch?v=RQWp...

Until recently, we thought that transporting a macroscopic cloud of particles a distance r in time t is suppressed by the usual LR-type light cone

exp(vt-r)

Turns out, the decay rate is proportional to the number of transported particles N

exp(N(vt-r))

arxiv.org/abs/2503.19788

Master in Mathematical Physics

If you're an undergraduate student interested in the mathematics of quantum physics and general relativity, consider the

Tübingen International M.Sc. Program in #MathematicalPhysics

www.math.uni-tuebingen.de/en/mmp

Opens for applications today

Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions We study sets of $δ$ tubes in $\mathbb{R}^3$, with the property that not too many tubes can be contained inside a common convex set $V$. We show that the union of tubes from such a set must have almos...

I am happy to announce that the Kakeya set conjecture, one of the most sought after open problems in geometric measure theory, has now been proven (in three dimensions) by Hong Wang and Joshua Zahl! arxiv.org/abs/2502.17655 I discuss some ideas of the proof at terrytao.wordpress.com/2025/02/25/t...

Had an amazing week at our Oberwolfach Mini-Workshop

"New Directions in Correlated Quantum Systems"

Huge thanks to our enthusiastic participants from both mathematics & physics!

ArXiv quant-ph needs to be split up! Paul Ginsparg lists Daniel Gottesman's proposed subcategories at his @aspenphysics.bsky.social talk. He is looking for feedback: please reply, dm, or email.

My colleague Mitia Duerinckx in Brussels is accepting applications for an open postdoc position in PDE & mathematical physics

It's funded by Mitia's ERC grant "PASTIS: Scaling limits of particle systems and microstructural disorder"

For more info, see mitia.duerinckx.web.ulb.be/postdoc-posi....

Uhlmann's theorem for relative entropies Uhlmann's theorem states that, for any two quantum states $ρ_{AB}$ and $σ_A$, there exists an extension $σ_{AB}$ of $σ_A$ such that the fidelity between $ρ_{AB}$ and $σ_{AB}$ equals the fidelity betwe...

Uhlmann's theorem states that the fidelity of two (mixed) states can be expressed in terms of their purifications (where the fidelity simplifies). In arxiv.org/abs/2502.01749 we generalize Uhlmann's theorem to Rényi relative entropies.

Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault...

To reach some consensus about the prospects of near-term (late nisq and early fault tolerant) quantum computing, we had a 3-day discussion event (“Quantum Now”) in Lapland with both optimists and pessimists. This continued at SeeQA 2024 in Oxford. See our conclusions here arxiv.org/abs/2501.05694

Local enhancement of the mean-field approximation for bosons We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance...

What is the propagation speed of Bose-Hubbard Hamiltonians when the initial state is a BEC?

We now have an answer in the mean-field regime (with applications to effective dynamics)

arxiv.org/abs/2412.13868

Thanks to my collaborators Simone Rademacher and Jingxuan Zhang!

Two open positions in mathematical physics in Tübingen
funded by ERC Starting Grant

"MathQuantProp: The Mathematics of Quantum Propagation"

Ph.D. position
www.mathjobs.org/jobs/list/26...

Postdoc position
www.mathjobs.org/jobs/list/26...

start: mid 2025 (flexible)
deadline: January 15, 2025

Enhanced Lieb-Robinson bounds for commuting long-range interactions Recent works have revealed the intricate effect of long-range interactions on information transport in quantum many-body systems: In $D$ spatial dimensions, interactions decaying as a power-law $r^{-α...

New preprint with Tom Wessel:

"Enhanced Lieb-Robinson bounds for commuting long-range interactions"

arxiv.org/abs/2411.19241

We observe that the power-law decay exponent required for a linear light cone improves from 2D+1 to 1 if the interactions are commuting. (Here D=spatial dim.)

A resolution of the Aharoni-Korman conjecture A poset $P$ is said to satisfy the finite antichain condition, or FAC for short, if it has no infinite antichain. It was conjectured by Aharoni and Korman in 1992 that any FAC poset $P$ possesses a ch...

A few days ago Lawrence Hollom posted a preprint that solves a problem about posets, informally known as the fishbone conjecture, which I am told was extremely central in the area. 🧵

arxiv.org/abs/2411.16844

Great idea! Please add me as well.

Workshop 16-20 December 2024

Workshop on

"Correlations of quantum many-body systems"

from Dec 16-20 at the University of Tübingen with excellent speakers:

sites.google.com/view/coqmbs/...

Deadline for submissions for contributed talks is Dec 1.

Thanks to Álvaro, Ángela, Sebastian and Simone for organizing this!