The elucidation of the way in which the additive and multiplicative structure of the integers are intertwined with one another is one of the most important and central themes in number theory. In August 2012, Shinichi Mochizuki (the proposer and chief organizer of the present RIMS Research Project) released preprints of a series of papers concerning "Inter-universal Teichmüller Theory", a theory that constitutes an important advance with regard to elucidating this intertwining. Moreover, the proof of the "ABC Conjecture", which follows as a consequence of the theory, attracted worldwide attention.

The present RIMS Research Project seeks to bring together various researchers not only from the "inter-universal Teichmüller theory community", but also researchers interested in various forms of mathematics related to inter-universal Teichmüller theory, and to provide all such researchers an opportunity to engage in lively discussions concerning the various developments.

This program is focused on the two-way interaction of logical ideas and techniques, such as definability from model theory and decidability from computability theory, with fundamental problems in number theory. These include analogues of Hilbert's tenth problem, isolating properties of fields of algebraic numbers which relate to undecidability, decision problems around linear recurrence and algebraic differential equations, the relation of transcendence results and conjectures to decidability and decision problems, and some problems in anabelian geometry and field arithmetic. We are interested in this specific interface across a range of problems and so intend to build a semester which is both more topically focused and more mathematically broad than a typical MSRI program.

Homological tools and ideas are pervasive in number theory. To defend this assertion, it suffices to evoke the role of étale cohomology in the study of the zeta functions of varieties over finite fields through the Weil conjectures, or the cohomological approach to class field theory formulated by Artin and Tate in the 1950's. The theory of motives, a manifestation of a universal cohomology theory attached to algebraic varieties, and the attendant motivic cohomology plays a central role in describing the special values of L-functions of varieties over number fields, via the conjectures of Deligne, Beilinson-Bloch, and Bloch-Kato. Much progress in the Langlands program exploits the fruitful connection between automorphic representations and the cohomology of associated Shimura varieties and more general arithmetic quotients of locally symmetric spaces. The study of special values of L-functions and the Langlands program, widely perceived as two fundamental yet seperate strands of the subject in the early 1990's, were beautifully unified in Wiles' epoch-making proof of the Shimura-Taniyama conjecture, in which this conjecture was reduced to a special instance of the Bloch-Kato conjecture for the symmetric square motive of an elliptic curve. Recent years have seen great strides in our understanding of the cohomology of the arithmetic quotients arising in the study of automorphic representations, spurred in part by the desire to extend the range of applicability of the celebrated Taylor-Wiles method. This has led to new automorphy and potential automorphy results: most spectacularly, perhaps, for abelian surfaces, as well as elliptic curves over general CM fields.

RNT will be a remote collaborative research experience for the weeks of October 5 through 18. The goal is for participants to learn new math, get to know colleagues, and have a joyful, affirming research experience. Workshop meetings will be planned around our busy schedules so that we can work on exciting research while also keeping up with our teaching and family responsibilities. We are anticipating groups working together Monday through Friday for on average 3 hours per day, though we encourage the members of each project to collaboratively design a work schedule that works for them. Note that the workshop will not have any events planned on the weekend or Monday, October 12, though some groups might want to work on these days if this is most convenient for them.

Team leaders have planned projects for participants to work on during the workshop. You can read more about the projects here:

https://sites.google.com/view/rethinkingnumbertheory/projects

To ensure that all participants can share in this joyful research experience, we ask that all who apply to participate be committed to equity and justice. We will also make time to imagine a different way to do math: How could hiring processes, grant writing, and conferences be transformed to be comfortable to everyone? We will have a code of conduct for the workshop, which you can read here:

https://sites.google.com/view/rethinkingnumbertheory/code-of-conduct

To participate in our workshop, please apply by the end of the day on September 20, 2020. The application is here:

https://sites.google.com/view/rethinkingnumbertheory/application

The 44th Midwest Representation Theory Conference will address recent progress in the theory of representations for groups over non-archimedean local fields, and connections of this theory to other areas within mathematics, notably number theory and geometry.

The conference will feature a sequence of contributed talks, and we especially encourage early-career participants from the broader Midwest region to apply. Review of applications will start on September 7. Please apply here: forms.gle/VgRq8m826T1SSmwk7

In order to receive information on how to participate (to be sent out closer to the conference), please register by October 14 here: forms.gle/zFAnQBnuPGRnKzMr7

If G is a reductive algebraic group over Z, the group G(Z) of its integral points (or any congruence subgroup thereof) acts discretely on the locally symmetric space X:= G(R)/K, where K is a maximal compact subgroup of G(R). The quotients G(Z) X play a fundamental role in the theory of automorphic forms and in number theory. Notably, their cohomology is a rich source of invariants attached to automorphic representations of G, and thus plays a central role in the Langlands program. A fundamental trichotomy governing the topological behaviour of such arithmetic quotients was proposed around 2010 by Bergeron and Venkatesh. A single positive integer d, depending only on the overlying symmetric space X, dictates the expected behaviour of the homology of the arithmetic quotient. When d=0, the cohomology is expect to have very little torsion but lots of characteristic 0 homology, which can be studied via analytic and transcendental methods (de Rham cohomology, Hodge theory). Shimura varieties and even-dimensional real hyperbolic spaces fall into this class. When d=1, one expects to find a lot of torsion but very little characteristic 0 homology. Odd dimensional hyperbolic manifolds, such as the Bianchi three-fold SL2(Z[i]) SL2(C)/U(2), fall into this case. When d is greater than 1, one expects little torsion and little characteristic zero homology.

There has been remarkable progress towards understanding how this trichotomy interacts with arithmetic: When d = 0, several interesting recent torsion-freeness results have been obtained by researchers like Caraiani, Emerton, Gee, and Scholze. When d=1, one can ask whether torsion always arises when it's expected to, and with the expected abundance. Torsion can be probed analytically using the Cheeger-Muller theorem. But there are obstructions ("tiny eigenvalues" and "very complex cycles"), which are very interesting in their own right, and need to be overcome in order to prove that there's as much torsion as expected. This torsion growth problem, especially for hyperbolic three-manifolds, has a life of its own even outside number theory, notably in the community of geometric groups theorists. Among the most striking developments arising in the relatively less well explored setting where d is larger than 1, let us mention Peter Scholze's construction of Galois representations attached to (possibly torsion) eigenclasses in the cohomology of arithmetic quotients, which is especially deep in this case. Another highly promising, fundamental breakthrough is manifested in Akshay Venkatesh's conjecture on derived Hecke algebras, which is expected to play an important role in extending the scope of the Taylor-Wiles method beyond the setting of d=0 to which it had been confined until relatively recently. The deep study of torsion in homology and analytic torsion carried out earlier by Bergeron, Venkatesh and others played a very important part in the nascent theory of derived Hecke operators and the attendant motivic action on the cohomology of arithmetic groups. In some very special instances, where G=GL(2) and one focusses on the coherent cohomology of an arithmetic quotient with values in certain automorphic sheaves, Venkatesh's conjectures exhibit a tantalising connection with certain ``tame refinements", in the spirit of conjectures of Mazur and Tate, of conjectures on the values of triple product p-adic L-functions.

The field is still in a very exploratory stage in which precise expectations (conjectural or otherwise) have not yet fully cristallised. For instance, there does not yet seem to be a reasonable conjecture about "how much cohomology", torsion or characteristic zero, to expect when d is greater than 1. Among other reasons, this makes computing in this setting very interesting. The workshop is expected to have a significant computational and experimental component, in which various experts will report on experimental data that might prove valuable in solidifying our expectations.

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.

The goal of this online workshop is to bring together some of the leading experts in the subject of arithmetic of L-values and Iwasawa theory to report on the latest developments.

The Banff International Research Station will host the "WIN5: Women in Numbers 5" workshop in Banff from November 15 to November 20, 2020.

Despite recent progress in gender equality in STEM fields, women continue to be underrepresented in the research landscape of many areas of mathematics, including number theory. The Women in Numbers (WIN) network was created in 2008 for the purpose of increasing the number of active female researchers in number theory. For this purpose, WIN sponsors regular conferences, taking place approximately every three years, where female scholars gather to collaborate on cutting-edge research in the field and produce publishable scientific results. The WIN workshops provide an ongoing forum for involving each new generation of junior faculty and graduate students in state-of-the-art research in number theory. They have to come be highly regarded among the broader number theory community due to the quality of research produced by these collaborations.

WIN5 is the fifth in this series of events, bringing together female number theorists at various career stages for research collaboration and mentorship. As always, the scientific program will centre on onsite collaboration on open research problems in number theory, conducted in small groups comprised of senior and junior scholars as well as graduate students. Groups will publish their initial finding in a peer-reviewed conference proceedings volume, and research partnerships formed at the WIN5 workshop are expected to last well beyond the duration of the event. WIN projects have the potential to grow into fruitful long-term research alliances that have a transforming influence on participants' careers and a significant positive impact on the research landscape in number theory. Past WIN workshop project groups have matured into highly effective research teams producing ongoing scholarly work of exceptional scientific quality.

The Casa Matemática Oaxaca (CMO) will host the "Langlands Program: Number Theory and Representation Theory" workshop in Oaxaca, from November 29 to December 04, 2020.

Langlands functoriality conjectures predict a vast generalization of the classical reciprocity laws of Class Field Theory, providing crossroads between Number Theory and Representation Theory. The conjectures are both local and global and pertain a connected reductive group and its Langlands dual group.

We aim to introduce young mathematicians in M\'exico and Latin-America to topics of current research in the Langlands Program. We will also promote the participation women and of graduate students from a diverse background in a workshop where experts in the field from across the world will gather to expand upon the frontiers of current research. In addition to research talks, there will be three courses that will also be accessible to mathematicians working in closely related fields.

The workshop will be devoted to the varied and fruitful interactions between p-adic cohomology theories, the theory of p-adic deformations of modular forms and Galois representations, and the construction of p-adic L-functions arising from the latter using techniques drawn from the former, with special emphasis on their rich array of arithmetic applications.

The field of p-adic automorphic forms has seen a huge development in the last decades with the construction of p-adic families in many new context. Among this one can cite Hansen's construction of eigenvarieties using overconvergent cohomology, and the coherent approach using (partial) Igusa towers of Andreatta–Iovita–Pilloni. There have been immediate applications to the construction of p-adic L-functions in families and to the proof of several instances of the conjectures by Greenberg and Benois on trivial zeroes, such as the work of Barrera–Dimitrov–Jorza.

But the existence of these eigenvarieties have proved to be useful also for the study of many other interesting arithmetic problems.

The first example is given by the applications to the Bloch–Kato conjecture. Bloch and Kato conjectured that the most interesting arithmetic information concerning varieties (and more generally, geometric Galois representations) are contained in two objects: the Selmer group and the L-function. They also conjecture that all the information coming from the Selmer group can be recovered from the L-function. Some special cases of this conjecture have been proven: we cite for example the work of Bellaiche–Chenevier for unitary groups and Skinner–Urban for elliptic curves in rank less or equal than 2. The key ingredients in these works is the use of deformations of automorphic forms and their Galois representations in p-adic families to construction elements in the Selmer group.

Another example is the study of local properties of Galois representations and the corresponding p-adic Hodge theory. We cite the work of Kedlaya, Pottharst, and Xiao concerning the existence of triangulations in families for p-adic representations of p-adic fields arising from finite slope automorphic forms. Other related results are the works on the smoothness of eigenvarieties at critical points by Bergdall and Breuil–Hellmann–Schraen; it has implication on the existence of companion forms, which are different p-adic automorphic forms sharing the same Galois representations (such as a CM form and its Serre antiderivative).

Very recently two new geometric approaches have been developed in the study of p-adic families and their L-functions.

Andreatta and Iovita introduced the idea of vector bundles with marked sections, which not only allows one to recover their previous constructions of eigenvarieties but let them p-adic interpolate in families the de Rham cohomology of the modular curve and the Gauss–Manin connection. They can then construct triple product p-adic L-functions for finite slope families and anticyclotomic p-adic L-functions when p is inert in the CM field.

At the same time, the introduction of perfectoid spaces and adic geometric has brought new and fresh ideas in the field: one can cite the new construction of classical eigenvarieties by Chojecki–Hansen–Johansson using functions on the perfectoid tower of modular curves and the construction by Kriz of a new p-adic Maass–Shimura operator and anticyclotomic p-adic L-functions in the inert case. His strategy relies on Scholze's Hodge to de Rham comparison isomorphism, which has been recently upgraded to an integral comparison map by Bhatt–Morrow–Scholze.

These new geometric tools have already allowed the construction of new p-adic L-functions; the aim of the workshop is to bring together arithmetic people with the experts in these two innovative approaches to find new exciting applications, both to global (Galois representations and their L-functions) and local (integral p-adic Hodge theory) problems.

This event builds upon a very successful series of previous conferences over the past 25 years. From the first event held in Bath in 1985 to the most recent one held in Birmingham in 2016 being as successful as its predecessors, the organising committee is delighted to announce the 12th IMA International Conference on Mathematics in Signal Processing to be held Monday 14 – Wednesday 16 December 2020 at Conference Aston, Aston University, Birmingham.

Signal processing and machine learning constitutes an important area for the application of mathematical concepts and techniques, in an era where learning algorithms must be transparent, robust, explainable and understandable, and ethical. It is a thriving area, as demonstrated by the success of the UK hosting the recent International Conference on Acoustics, Speech, and Signal Processing (ICASSP) in Brighton in 2019.

Signal and information processing is at the heart of our technological world, fuelled by developments in, for example, mobile communications, networks and graphs, multimedia systems, medical image analysis, genomics and bioengineering, neural signal processing, big data processing and internet of things. The aim of the conference is to bring together mathematicians, statisticians and engineers with a view to exploring recent developments in mathematics for signal processing and machine learning and identifying fruitful avenues for further research. It is hoped that the meeting will help to attract more mathematicians into this important and challenging field.

The conference will follow the same successful format as our previous conferences, comprising of tutorials, keynote addresses and non-overlapping technical sessions consisting of oral and poster presentations. A social programme will be organised and will include a reception to welcome delegates. Call for Papers Contributed papers are invited on all aspects of mathematics in signal processing and will be accepted on the basis of a 300?500 word abstract which should be submitted by 13 July 2020 via https://my.ima.org.uk. The majority of contributed papers will be presented in the poster sessions. Successful authors will be invited to submit a four page paper for inclusion in the conference proceedings by 2 November 2020. Note: If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in.

Papers describing the application of mathematical developments in Signal Processing and Machine learning for physical modelling, communications, financial modelling, medicine, meteorology, radar, seismology, sonar, ocean science, multimedia, instrumentation and control, audio, and acoustics, etc., are invited:

• Applications of Finite Mathematic • Nonlinear Optimisation/Modelling • Blind Deconvolution / Equalisation • Approximation Techniques • Time-frequency / Time-scale Analysis • Space-Time Adaptive Signal Processing • Vector Sensors and Geometric Processing • High Resolution Spectral Analysis • Graph Signal Processing • Signal Processing aspect of digital communications • Simultaneous localisation and mapping • Inference for diffusion processes • Statistical Signal Processing • Compressive Sampling • Graph Signal Processing • Inverse Problems • Adaptive Signal Processing • Numerical Linear Algebra • Machine Learning, including Deep Learning • Audio/Image/Video Processing • Array Signal Processing • Bayesian Signal Processing • Signal Separation Techniques

Registration for this Conference is currently open at https://my.ima.org.uk/ If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in. Early Bird Conference Fees Non IMA Member - £430 IMA Member - £320 Student Member - £210 Student Non Member - £220 Please note: all Conference Fees will increase by £20 on 11 November 2020 Conference Dinner: There will be a Conference Dinner held at Conference Aston on 15 December. The dinner costs £45 and is available as an add-on option when you register. Please inform us of any dietary requirements when booking.

Day Delegate rate: A Day Delegate rate is also available for this Conference if you would like to attend one of the scheduled Conference days. If you would like to find out more information about our Day Delegate rate, please contact us at conferences@ima.org.uk

Accommodation: Further information regarding booking accommodation at Conference Aston will be released shortly.

Organising committee James R. Hopgood (Chair), University of Edinburgh Jonathon Chambers, University of Leicester Malcolm Macleod, QinetiQ

The aims of this conference is to provide a platform for the scientists, scholars, engineers and students from the universities all around the world and the industry to present ongoing research activities.

Combinatorial algebraic geometry comprises the parts of algebraic geometry where basic geometric phenomena can be described with combinatorial data, and where combinatorial methods are essential for further progress.

Research in combinatorial algebraic geometry utilizes combinatorial techniques to answer questions about geometry. Typical examples include predictions about singularities, construction of degenerations, and computation of geometric invariants such as Gromov-Witten invariants, Euler characteristics, the number of points in intersections, multiplicities, genera, and many more. The study of positivity properties of geometric invariants is one of the driving forces behind the interplay between geometry and combinatorics. Flag manifolds and Schubert calculus are particularly rich sources of invariants with positivity properties.

In the opposite direction, geometric methods provide powerful tools for studying combinatorial objects. For example, many deep properties of polytopes are consequences of geometric theorems applied to associated toric varieties. In other cases geometry is a source of inspiration. For instance, long-standing conjectures about matroids have recently been resolved by proving that associated algebraic structures behave as if they are cohomology rings of smooth algebraic varieties.

Much research in combinatorial algebraic geometry relies on mathematical software to explore and enumerate combinatorial structures and compute geometric invariants. Writing the required programs is a considerable part of many research projects. The development of new mathematics software is therefore prioritized in the program.

The program will bring together experts in both pure and applied parts of mathematics as well mathematical programmers, all working at the confluence of discrete mathematics and algebraic geometry, with the aim of creating an environment conducive to interdisciplinary collaboration. The semester will include four week-long workshops, briefly described as follows.

• A 'boot-camp' aimed at introducing graduate students and early-career researchers to the main directions of research in the program.

• A research workshop dedicated to geometry arising from flag manifolds, classical and quantum Schubert calculus, combinatorial Hodge theory, and geometric representation theory.

• A research workshop dedicated to polyhedral spaces and tropical geometry, toric varieties, Newton-Okounkov bodies, cluster algebras and varieties, and moduli spaces and their tropicalizations.

• A Sage/Oscar Days workshop dedicated to development of programs and software libraries useful for research in combinatorial algebraic geometry. This workshop will also feature a series of lectures by experts in polynomial computations.

This workshop will focus on the development of software to facilitate research in combinatorial algebraic geometry, based on the SAGE Mathematical Software System and the OSCAR Computer Algebra System. Special attention will be given to efficient computations with multi-variate polynomials, which is a critical part of many algorithms in combinatorial algebraic geometry. Aside from development of software, the workshop will feature a series of talks about polynomial computations, as well as introductory lectures about Sage and Oscar.

Science and technology play an increasingly important role in supporting the defence and security industries. Mathematics is fundamental to these two disciplines, providing a framework for understanding and solving the varied and complex problems faced, and to model systems and scenarios. These models are then used to estimate system performance, find weaknesses in real systems, and suggest improvements. This conference brings together a wide variety of mathematical methods with defence and security applications. The programme will include keynote speakers, presentations and poster sessions, as well as refreshment breaks for informal discussions. It is aimed towards mathematicians, scientists and engineers from both industry and academia, in addition to government and military personnel who have an interest in how mathematics can be applied to defence and security problems. This will be the sixth Mathematics in Defence and Security, conference albeit the first with ‘Security’ explicitly mentioned in the title; the previous conferences each attracted over 100 delegates from a wide range of organisations including Dstl, QinetiQ, AWE, BAE Systems, Thales, Rolls Royce, the IMA, the MoD, academia and international parties. Keynote and Invited Speakers: Keynote and Invited Speakers will be announced closer to the date of the conference. If you have any queries, please contact the Conference Department. Call for Papers - Closed The Call for Papers for this Conference is closed. This is an open conference and all papers and presentations will be unclassified. The proceedings will be made available to delegates on USB and for download from the conference webpage.

Registration is currently open at https://my.ima.org.uk/ If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in.

Early Bird Conference Fees:

Non IMA Member - £185

IMA Member - £135

IMA Student - £85

Non-Member Student - £95

Please note: conference fees will increase by £20 on 28 February 2021.

Organising Committee Edward Rochead (Dstl) Chair Kevin Wagstaff (Dstl) Richard Hoyes (Dstl) Alexandra Tzella (University of Birmingham)

The conference “Analytic Number Theory, Quantum Chaos and their Interfaces” aims at gathering distinguished researchers working in either of the disciplines to discuss recent research advances in these fields, and serve as a playground for the exchange of ideas between these, rather diverse, research communities. Another purpose of our conference is to provide a solid educational platform for more junior researchers (PhD students, postdoctoral researchers and early career permanent faculty) who aspire to conduct research in the relevant fields and expose them to some of the outstanding results and open problems as well as to meet other researchers with similar academic interests, with high potential to start new research collaborations. Being a home to Professor Zeev Rudnick, who has contributed greatly to unifying the main subjects of the conference and established some relevant fundamental results in these fields, Tel Aviv University is a natural place for such a meeting to take place.

In the fall semester of 1985, Prof. Jean-Pierre Serre taught at Harvard University an extended series of lectures of his course on Rational Points on Curves over Finite Fields , first taught at Collège de France. Fernando Gouvêa's handwritten notes of this course have been spread all around since then. These notes contain the origin and inspiration of most of the works on the topic since 1985: maximal curves, construction of curves from their jacobians, class field towers, asymptotics of the number of points, etc.

At last, these notes have been edited, revised and are going to be published by the Société Mathématique Française in the Documents Mathématiques series. The present workshop will celebrate the publication of these notes. Experts on the topic will explain the main progress since 1985 and will discuss open questions and new techniques on curves over finite fields. Plenary speakers will be asked to write down their talks in order to publish proceedings which will be a natural continuation of Serre’s book.

Our goal is to organise a conference devoted to interactions between pure mathematics (in particular arithmetic and algebraic geometry) and information theory (especially cryptography and coding theory). This conference will be the eighteenth edition, with the first one held in 1987, in a series that has traditionally brought together some of the top specialists in the domains of arithmetic, geometry, and information theory. The corresponding international community is very active and all of the concerned research domains are developing and expanding rapidly.

The conference is therefore also an important occasion for junior mathematicians (graduate students and postdocs) to interact with established researchers in order to exchange ideas. We aim to create an inclusive atmosphere and to encourage forging new connections between researchers of various different backgrounds.

The conference talks will be devoted to recent advances in arithmetic and algebraic geometry and number theory, with a special emphasis on algorithmic and effective results and applications of these fields to information theory.

The conference will last one week and will be organized as follows :

• There will be one or two plenary talks each day, at the start of each session. They will be given by established researchers, some of whom are new to the established AGC2T community; this will allow for the introduction of emerging topics to the community, which may give rise to applications of arithmetic or algebraic geometry to information theory.
• There will be several shorter specialized talks in each session, often delivered by junior mathematicians.

As with the previous editions of the AGC2T, we aim publish conference proceedings as a special volume of the Contemporary Mathematics collection of the AMS.

Conference Topics

• Algebraic and arithmetic geometry over finite fields and global fields.
• Number theory, especially explicit and algorithmic.
• Algebro-geometric codes constructed from curves and higher-dimensional algebraic varieties over finite fields and global fields.
• Arithmetic and geometric aspects of cryptography (symmetric, public key, and post-quantum) and cryptanalysis.

Young Researchers in Mathematics is the conference for all PhD students in the UK. We want to welcome each and every early career mathematician to this conference, where you can meet researchers from all areas in a friendly environment. YRM is the perfect opportunity to give talks about your maths, whether it be introductory or your own results. We also invite you to the plenary talks, which showcase a wide range of mathematics happening in the UK now. Please note the change of dates.

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.

In arithmetic geometry, one studies solutions to polynomial equations defined with arithmetically interesting coefficients, such as integers or rational numbers. One way to study such objects, which has seen tremendous success in the last several decades, is by investigating their symmetries. Quite surprisingly, in several interesting situations, many of the geometric and arithmetic properties of the objects in question are actually controlled by the object’s symmetries.

Unfortunately, it is usually impossible to study these symmetries directly with current technology. To get around this, mathematicians working in this area often study simplified (often linearized) versions of the symmetries in question, which still capture a significant amount of information about the given object. This workshop will bring together both senior and junior researchers, including graduate students, postdocs, and leading experts, who study objects of geometric and arithmetic origin from the point of view of their symmetries and their linearized variants.

There is an age-old relationship between arithmetic and geometry, going back at least to Euclid's Elements. Historically, it has usually been geometry that has been used to enrich our understanding of arithmetic, but the purpose of this workshop is to study the flow of information in the other direction. Namely, how can arithmetic enhance our understanding of geometry? This meeting will bring together researchers from both sides of the partnership, to explore ways to bind the two fields ever closer together.

One focus of modern number theory is to study symmetries of numbers that are roots of polynomial equations. Collections of such symmetries are called Galois groups, and they often encode interesting arithmetical information. The theory of Galois representations provides a way to understand these Galois groups and in particular, how they interact with other areas of mathematics. This workshop will investigate how these Galois representations can be put together into families, and search for new arithmetic applications of these families.

The workshop will bring together people attacking key problems in number theory via techniques involving concrete or computable descriptions. Here, number theory is interpreted broadly, including algebraic and analytic number theory, Galois theory and inverse Galois problems, arithmetic of curves and higher-dimensional varieties, zeta and L-functions and their special values, and modular forms and functions. Considerable attention is paid to computational issues, but the emphasis is on aspects that are of interest to the pure mathematician.

During the last two weeks of July 2021, the University of Oregon will host a graduate instructional workshop followed by a collaborative research workshop to promote diverse collaborations.

While both of these workshops focus on algebraic and p-adic aspects of automorphic forms, L-functions, and related topics, the two workshops are independent. Applicants are encouraged to apply for one or both of the workshops, and funding decisions will be determined separately for each.

This workshop aims at bringing together the leading experts in the field, covering a broad spectrum reaching from the more theoretically-oriented over the explicit to the algorithmic aspects. The fundamental problem motivating the workshop asks for a description of the set of rational points X(Q) for a given algebraic variety X defined over Q. When X is a curve, the structure of this set is known, and the most interesting question is how to determine it explicitly for a given curve. When X is higher-dimensional, much less is known about the structure of X(Q), even when X is a surface. So here the open questions are much more basic for our understanding of the situation, and on the algorithmic side, the focus is on trying to decide if a given variety does have any rational point at all.

This is a workshop with about 50 participants. Participation is by invitation. Every participant is expected to contribute actively to the success of the event, by giving talks and/or by taking part in the discussions.

Algebraic dynamics is the study of discrete dynamical systems on algebraic varieties. It has its origins in complex dynamics, where one studies self-maps of complex varieties, and now encompasses dynamical systems defined over global fields.

In recent years, researchers have fruitfully investigated the latter by applying number-theoretic techniques, particularly those of Diophantine approximation and geometry, subfields which study the metric and geometric behavior of rational or algebraic points of a variety. The depth of this connection has allowed the mathematical arrow between the two fields to point in both directions; in particular, arithmetic dynamics is providing new approaches to deep classical Diophantine questions involving the arithmetic of abelian varieties. This workshop will focus on communicating and expanding upon the connections between algebraic dynamics and Diophantine geometry. It will bring together leading researchers in both fields, with an aim toward synthesizing recent advances and exploring future directions and applications.

The GTA 2021 conference will bring together world class researchers in mathematics. Its main objectives are to discuss recent advances in the fields of algebraic geometry, number theory and their applications, as well as to foster international collaborations on connected topics.

Although contributions from all related areas of mathematics are welcome, particular emphasis will be placed on research interests of our late colleague Alexey Zykin, namely: zeta-functions and L-functions, algebraic geometry over finite fields, families of fields and varieties, abelian varieties and elliptic curves.

Despite the enormous commercial potential that quantum computing presents, the existence of large-scale quantum computers also has the potential to destroy current security infrastructures. Post-quantum cryptography aims to develop new security protocols that will remain secure even after powerful quantum computers are built. This workshop focuses on isogeny-based cryptography, one of the most promising areas in post-quantum cryptography. In particular, we will examine the security, feasibility and development of new protocols in isogeny-based cryptography, as well as the intricate and beautiful pure mathematics of the related isogeny graphs and elliptic curve endomorphism rings. To address the goals of both training and research, the program will be comprised of keynote speakers and working group sessions.

A conference on the occasion of Takeshi Saito's 60th birthday

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.

The success of modern codes for large-scale optimization is heavily dependent on the use of effective tools of numerical linear algebra. On the other hand, many problems in numerical linear algebra lead to linear, nonlinear or semidefinite optimization problems. The purpose of the conference is to bring together researchers from both communities and to find and communicate points and topics of common interest. This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM). Conference topics include any subject that could be of interest to both communities, such as: • Direct and iterative methods for large sparse linear systems. • Eigenvalue computation and optimization. • Large-scale nonlinear and semidefinite programming. • Effect of round-off errors, stopping criteria, embedded iterative procedures. • Optimization issues for matrix polynomials • Fast matrix computations. • Compressed/sparse sensing • PDE-constrained optimization • Distributed computing and optimization • Applications and real time optimization Invited Speakers Invited Speakers to be confirmed shortly. Registration Registration is currently open at https://my.ima.org.uk/ If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in. Call for Papers and Mini-Symposiums Mini-symposium proposals and contributed talks are invited on all aspects of numerical linear algebra and optimization. Mini-symposium proposals should be submitted to conferences@ima.org.uk by 31 January 2022. A mini-symposium consists of up to four speakers. For emerging topics the mini-symposium can be extended to at most two sessions on a single topic (maximum eight speakers). Organisers will be advised of acceptance by 14 February 2022. Contributed talks and mini-symposia talks will be accepted on the basis of a one page extended abstract which should be submitted by 28 February 2020 online at http://online.ima.org.uk/ or by e-mail to conferences@ima.org.uk. Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference. Key deadlines Mini-symposia proposals: 31 January 2022 Notification of acceptance of mini-symposia: 14 February 2022 Abstract submission: 28 February 2022 Notification of acceptance of abstracts: 31 March 2022 Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference.

Early Bird Conference Fees IMA/SIAM Member - £395.00 Non IMA/SIAM Member - £450.00 IMA/SIAM Student - £215.00 Non IMA/SIAM Student - £225.00 Conference Fees will increase by £20 on 22 May 2022 Day Delegate rate: A Day Delegate rate is also available for this Conference if you would like to attend one of the scheduled Conference days. If you would like to find out more information about our Day Delegate rate, please contact us at conferences@ima.org.uk

Accommodation The IMA have booked accommodation at Edgbaston Park Hotel on hold for delegates on a first-come, first-serve basis. The room is £90 Single occupancy, B&B which will be available to book until 16/05/2022. If you are interested in booking at this rate, please contact the Conferences Department for the booking code.

Organising Committee Michal Kocvara, University of Birmingham (co-chair) Daniel Loghin, University of Birmingham (co-chair) Coralia Cartis, University of Oxford Nick Gould, Rutherford Appleton Laboratory Philip Knight, University of Strathclyde Jennifer Scott, Rutherford Appleton Laboratory Valeria Simoncini, University of Bologna Contact information For general conference queries please contact the Conferences Department, Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK. E-mail: conferences@ima.org.uk Tel: +44 (0) 1702 354 020