The Mathematics Research Communities program, run by AMS, is a great opportunity for young researchers to get involved in new research projects. It is a professional development program offering a chance to be part of a network. The program is described at http://www.ams.org/programs/research-communities/mrc-20 .

Marni MISHNA, Stephen MELCZER, Robin PEMANTLE are organizing a MATHEMATICAL RESEARCH COMMUNITY the week of May 31 - June 6, 2020 on the theme of Combinatorial Applications of Computational Geometry and Algebraic Topology. Yuliy BARYSHNIKOV and Mark WILSON will be assisting as well in the running of the workshop and the applied mathematics mentoring activities.

A brief description of MRC is at the site: https://www.ams.org/programs/research-communities/2020MRC-CompGeom . It is a great chance to learn some new techniques and crossover to a new community. Note the cross-disciplinary nature: the topic draws on combinatorics, singularity theory, algebraic topology, and computational algebra.

Young researchers who will be between -2 and +5 years post Ph.D. in Summer 2020 are encouraged to apply.

Applications are being accepted from now through February at the site https://www.mathprograms.org/db/programs/826 .

The 37th Annual Workshop in Geometric Topology will be held June 4-6, 2020 at Texas Christian University in Fort Worth, Texas. The featured speaker will be Andy Putman of the University of Notre Dame, who will give a series of three one-hour lectures on the Topology of Moduli Spaces. Participants are invited to contribute talks of 20 to 30 minutes.

Full details can be found at the conference web site at http://faculty.tcu.edu/gfriedman/GTW2020

Financial support is available to help defer travel and local expenses. Graduate students, recent PhDs in geometric topology, and members of underrepresented groups in mathematics are especially encouraged to apply for support. Funding for the workshop is provided by a grant from the National Science Foundation (DMS-1764311), by the TCU College of Science and Engineering, and by the TCU Department of Mathematics.

Important deadlines: Requests for financial support (to receive full consideration): April 17 Reservation and payment for housing on TCU campus: May 1 Submission of contributed talks, including title and abstract: May 1

Please contact Greg Friedman (g.friedman@tcu.edu) if you have any questions.

Workshop Organizers: Fredric Ancel, University of Wisconsin-Milwaukee; Greg Friedman, Texas Christian University; Craig Guilbault, University of Wisconsin-Milwaukee; Molly Moran, Colorado College; Nathan Sunukjian, Calvin College; Eric Swenson, Brigham Young University; Frederick Tinsley, Colorado College; Gerard Venema, Calvin College

With this workshop we would like to promote the interaction between the following five fields:

• Berkovich spaces,
• Tropical geometry,
• p-adic differential equations,
• Arithmetic D-modules and representations of p-adic Lie groups,
• Arithmetic applications of p-adic local systems.

While the first two are already tightly linked, the role of Berkovich spaces in the last 3 topics is only emerging and within this, the role of tropical geometry has not yet been explored. More generally, we consider this conference to be a good opportunity to study new techniques recently introduced into the field. We are convinced that each of these areas has plenty of potential and that a fruitful interaction between them might nourish their development. The aim of the conference is precisely to give leading experts in these each of these domains the opportunity to meet, present their last results and open challenges, and encourage an exchange that will drive forward these exciting and rapidly developing subjects.

A poster session is planned. Students are welcome to submit posters.

Topic: A primary aim of chromatic homotopy theory is to understand the stable homotopy category by decomposing it into pieces (called chromatic localizations) which are, at least in principle, easier to understand. These chromatic localizations enjoy a certain duality property called ambidexterity, which guarantees that certain homotopy limits can be understood as homotopy colimits (and vice versa). The goal of this workshop is to explain the mathematics of ambidexterity and some of its applications.

A preliminary syllabus and live application is available at the website.

Suggested prerequisites: Some knowledge of chromatic homotopy theory will be expected; while the workshop will feature a review lecture on the topic, this will be insufficient if the topic is entirely new to participants. Additionally, participants should have familiarity with the language of infinity categories.

Mentors: The 2020 Talbot workshop will be mentored by Prof. Jacob Lurie of the IAS and Prof. Tomer Schlank of The Hebrew University of Jerusalem.

Format: The workshop discussions will have an expository character and most of the talks will be given by participants. The afternoon schedule will be kept clear for informal discussions and collaborations. The workshop will take place in a communal setting, with participants sharing living space and cooking and cleaning responsibilities.

Funding: We cover all local expenses, including lodging and food. We also have limited funding available for participant travel costs.

Who should apply: Talbot is meant to encourage collaboration among young researchers, particularly graduate students. To this end, the workshop aims to gather participants with a diverse array of knowledge and interests, so applicants need not be an expert in the field. In particular, students at all levels of graduate education are encouraged to apply. Our decisions are based not on applicants' credentials but on our assessment of how much they would benefit from the workshop. As we are committed to promoting diversity in mathematics, we also especially encourage women and minorities to apply.

The purpose of this meeting is to bring together a diverse range of experts and early-career researchers working in in a variety of aspects of the study of holomorphic curves and their applications to low-dimensional topology. Points of focus will include contact and symplectic structures and dynamics, Lagrangian cobordisms and Legendrian knots, and Floer–theoretic frameworks of study.

Andrew Ranicki and his theory of algebraic surgery played a central role in linking manifold theory, algebraic K-theory, and its close cousin L-theory. These areas have seen great developments and advances in the last decade from distinct research communities. This workshop will bring together mathematicians working on the topology of high-dimensional manifolds and their automorphisms with those working on the algebraic K-theory (and its cousins hermitian K-theory and L-theory) of rings and ring spectra, in order to share recent progress in these areas and kindle a fresh interaction between them.

The lecture series and research talks at the IHES Summer School will focus on presenting the latest developments in topics related to categories of motives, calculational and foundational aspects of motivic and equivariant homotopy theory, and the generalisations of these tools and techniques in the setting of non-commutative geometry.

See conference website

Transchromatic phenomena appear in a variety of contexts. These include stable and unstable homotopy theory, higher category theory, topological field theories, and arithmetic geometry. The aim of the conference is to bring together people from all of these areas in order to understand the relationship between each others work and to further demystify the appearance of transchromatic patterns in such disparate areas.

Homotopical and higher categorical methods have seen increasing importance in mathematics, both as foundations and as computational tools. In fact, such methods merge two apparently distinct goals: understanding geometrical forms and classifying mathematical structures. This conference aims at gathering together under this perspective geometers in a rather broad sense. It seeks to foster the applications of these higher methods in the interplay between homotopy theory, arithmetic, and algebraic geometry.

The conference is supported by the SFB1085 "Higher Invariants -Interactions between Arithmetic Geometry and Global Analysis"

Applied and computational topology, one of the most rapidly growing branches of mathematics, is becoming a key tool in applied sciences. It is making impact not only in mathematics, but on the wide interdisciplinary environment including material and medical sciences, data science, robotics. Building upon successful conferences held in Bedlewo in 2013 and 2017, the next edition of Applied Topology in Bedlewo will take place in 2021. Similarly as before, our aim is to bring together scientists from all over the world working in various fields of applied topology. This time we will focus on:

• random topology,
• topological methods in combinatorics,
• topological data analysis and shape descriptors,
• topological analysis of time-varying data in biology, engineering and finance,
• topological and geometrical descriptors of porous materials.

This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM).

Areas of interest include, but are not limited to: Topology. Kinematics. Algebraic topology of con?guration spaces of robot mechanisms. Topological aspects of path planning and sensor networks. Differential topology and singularity theory of robot mechanism and moduli spaces. Algebraic Geometry. Varieties generated by linkages and constraints. Geometry of stiffness and inertia matrices. Rigid-body motions. Computational approaches to algebraic geometry. Dynamical Systems and Control. Dynamics of robots and mechanisms. Simulation of multi-body systems, e.g. swarm robots. Geometric control of robots. Optimal control and other optimisation problems. Combinatorial and Stochastic Methods. Rigidity of structures. Path planning algorithms. Modular robots. Statistics. Stochastic control. Localisation. Navigation with uncertainty. Statistical learning theory. Cognitive Robotics. Mathematical aspects of Artificial Intelligence, Developmental Robotics and other Neuroscience based approaches.

Invited speakers: Dr Mini Saag – University of Surrey, UK Prof Frank Sottile - Texas A&M University, USA Prof Stefano Stramigioli - University of Twente, The Netherlands

A lattice is a discrete collection of regularly ordered points in space. Lattices are everywhere around us, from the patterned stacked arrangements of fruits and vegetables at the grocery to the regular networks of atoms in crystalline compounds. Today lattices find applications throughout mathematics and the sciences, applications ranging from chemistry to cryptography and Wi-Fi networks.

The focus of this meeting is the connections between lattices and number theory and geometry. Number theory, one of the oldest branches of pure mathematics, is devoted to the study properties of the integers and more sophisticated number systems. Lattices and number theory have many deep connections. For instance using number theory it was recently demonstrated that certain packings of balls in high dimensions are optimally efficient. Lattices also appear naturally when one studies certain spaces that play an important role in number theory; one of the main focuses of this meeting is to investigate computational and theoretical methods to understand such spaces and to expand the frontier of our algorithmic knowledge in working with them.

The cohomology of arithmetic groups is the study of the properties of ``holes'' in geometric spaces that contain information about number theory. The workshop will bring together mathematicians with expertise in number theory, topology, and geometric group theory to tackle these problems and explore recent developments.