### Conveners

#### Plenary

- Francesca Cuteri (Goethe Universitรคt)

#### Plenary

- Bipasha Chakraborty (University of Cambridge)

#### Plenary

- Kari Rummukainen (University of Helsinki)

#### Plenary

- Chris Monahan (William & Mary)

#### Plenary

- Xu Feng (Peking University)

#### Plenary

- Christoph Lehner (University of Regensburg & Brookhaven National Laboratory)

In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD. This talk will focus on the developments in the last few years. Especially the addition of external influences and extended ranges of $T$ and $\mu$ yield an increasing number of interesting results, a subset of which will be discussed. Many of these conditions are important for the...

New incarnations of heavy-ion collision experiments are turning our attention to hard processes and a more fine-grained resolution of the QGP. In this endeavor quarkonia or open heavy flavors turn out to be versatile probes, which are usually described through models based on perturbative QCD, AdS, and effective field theories. The lattice provides nonperturbative input and constraints to such...

I will discuss the RBC & UKQCD collaboration's recent lattice calculation of $\epsilon'$, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4x the statistics and more reliable systematic error estimates. I will also discuss how our results demonstrate the Standard Model origin of the $\Delta I=1/2$ rule, and will...

The CabibboโKobayashiโMaskawa (CKM) matrix element $|V_{ub}|$ describes the coupling between $u$ and $b$ quarks in the weak interaction, and is one of the fundamental parameters of the Standard Model. $|V_{ub}|$ is the focus of a longstanding puzzle, as the world-average values derived from inclusive and exclusive $B$-meson decays show a tension of a few standard deviations.

Semileptonic...

Exotic states have been predicted before and after the advent of QCD.

In the last decades they have been observed at accelerator experiments in the sector with two heavy quarks, at or above the quarkonium strong decay threshold and called X Y Z states.

These states offer a unique possibility for investigating the dynamical properties of strongly correlated systems in QCD.

I will show how...

This talk will offer an overview of the role of lattice field theory in strongly interacting BSM phenomenology.

I discuss progress in simulating field theories on discrete hyperbolic spaces, with the goal of studying their physics in the bulk, and on the boundary. At tree-level, a free scalar field propagating in the bulk lattice is found to possess power-law two-point correlation functions on the boundary. The power-law behavior excellently matches the expected Klebanov-Witten formula despite being...

The lattice community, and more widely the physics community, has a long track record of using and even building advanced Statistical & Machine Learning tools (e.g. HMC). On the other hand, the Machine Learning, and specifically the Deep Learning, community has itself been seeking inspiration from Physics. Geometry and symmetries are inspiring many ML papers and research directions. Those...

Using variational methods for QFT at strong coupling is an ancient dream with multiple concrete approaches. We discuss recent work on a particular approach, Lightcone Conformal Truncation, that uses lightcone quantization in infinite volume and a truncated Hilbert space motivated by the conformal symmetry of an ultraviolet fixed point at the upper end of an RG flow containing the QFT of interest.

The underrepresentation of women and BIPOC individuals in STEM in the U.S. is a well-known and long-standing problem. Among the most robust explanations for this underrepresentation is social and structural bias against non-prototypical members of these fields (e.g., Moss-Racusin et al., 2012). In this talk, I extend what we know about unidimensional gender bias or racial bias in STEM and...

The US electron ion collider (EIC) was established firmly as a project in the Office Of Science in January 2020. The EIC will be built at Brookhaven National Laboratory (BNL) jointly by BNL and Jefferson Lab working as partners. An EIC Project has been setup and is making progress fast. The EIC Users Group is evolving in to proto-collaborations which are expecting to submit preliminary...

We review the latest progress in lattice QCD calculations of the partonic structure of hadrons. This structure is, in particular, described in terms of *x*-dependent distributions, the simplest of which are the standard parton distribution functions (PDFs). The lattice calculations rely on matrix elements probing spatial correlations between partons in a boosted hadron, that can be matched to...

The form factors of the nucleon provide key information on nucleon properties and processes. When confronted with precisely measured observables from experiment, they serve as benchmark quantities for lattice calculations. On the other hand lattice determinations may serve as vital theory input for the interpretation of experiments, e.g. in neutrino-nucleus scattering. I will review recent...

Lattice QCD spectroscopy and subsequent determinations of scattering amplitudes are an active line of research with notable advances. In the two-hadron sector there has been significant progress in constraining more complicated scattering amplitudes as well as in controlling systematic uncertainties. A new frontier is the practical application of finite-volume formalisms to treat three-hadron...

In recent years, the lattice effective field theory, a lattice stochastic methods, were successfully applied in solving the nuclear many-body problems. It has shown great advantages in simulating from first principles the atomic nuclei at ground state and excited states, nuclear scattering and reaction, nuclear matter at zero and finite temperature, etc. In this talk, I will give a brief...

The supercomputer "Fugaku" was jointly developed by Fujitsu Limited and RIKEN, and is the latest supercomputer installed at the RIKEN Center for Computational Science in Kobe, Japan. In the recent Top500, HPCG, and HPL-AI benchmark rankings, it has been ranked No. 1 in the world for two consecutive terms (June 2020 and November 2020). The CPU installed in Fugaku is a 48-core + 2 assistant core...

In this joint venture between mathematicians and physicists, we develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings, motivated by models in lattice gauge theory. A novel element of this work is the potential benefit in using a family of numerical integration methods called "lattice cubature rules"....

The Atiyah-Singer(AS) index theorem on a closed manifold is well understood and appreciated in physics. On the other hand, the Atiyah-Patodi-Singer(APS) index, which is an extension to a manifold with boundary, is physicist-unfriendly, in that it is formulated with a nonlocal boundary condition. Recently we (3 physicists and 3 mathematicians) proved that the same index as APS is obtained from...

The tensor renormalization group (TRG) is a promising approach to study various models of lattice field theory.

In particular, we can easily realize numerical calculations

for theories with the sign problem, and on extremely large volume lattices, by the method. In this talk, I will review the recent progress in the TRG method.

We compute the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. The calculations are performed using four flavors of stout smeared staggered quarks, with quark masses at their physical values. The continuum limit is taken using six different lattice spacings ranging from $0.132\,\text{fm}$ down to $0.064\,\text{fm}$. All strong isospin...

In this talk I will review some of the trends in computing systems

including discussing the new and upcoming systems in the U.S. and elsewhere as information allows. I will also discuss some of the programming models to develop software for these systems with an emphasis on portable, and where possible, performance portable approaches.

A beautiful description of natureโs fundamental forces has been devised through gauge fields introducing local symmetries or conserved charges. While classical techniques continue to provide invaluable information on the emergent properties of gauge field theories relevant to experimental programs throughout the scientific domains, some experimentally relevant parameter regimes (e.g., where...