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"

The Cascade Topology Seminar is a semi-annual conference ordinarily serving topologists of all stripes in the Pacific Northwest and western Canada. This fall's iteration is being held online. It will consist of 6 topology talks spread over 3 days, in the morning (Pacific time). Everyone with an interest in topology is welcome.

The Thirteenth Annual Binghamton University Graduate Conference in Algebra and Topology (BUGCAT) will be held online on November 7-8, 2020. This conference is organized and run by mathematics graduate students of Binghamton University. We are hoping that during this time of crisis, we could still provide an opportunity for graduate students to talk math, connect with other students and faculty, present your research and share our spirits. There will be multiple sessions with 30-minute talks given by students and faculties. This year we have three distinguished keynote speakers: Emily Riehl (Johns Hopkins University), Moshe Cohen (SUNY New Paltz) and Ben Steinberg (The City University of New York).

Registration is now open! For registration and other information, please visit our website. The deadline for submitting a talk is October 21st. The deadline for requesting funding is October 2nd.

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.