
Critical Issues in Mathematics Education 2019: Mathematical Modeling in K16: Community and Cultural Contexts
Organizers: Julia Aguirre (University of Washington  Tacoma), LEAD Cynthia Anhalt (University of Arizona), Staffas Broussard (The Algebra Project), Ricardo Cortez (Tulane University), Michael Driskill (Math for America ), Sol Garfunkel (Consortium for Mathematics and Its Applications (COMAP)), Genetha Gray (Salesforce), Maria Hernandez (North Carolina School of Science and Mathematics), LEAD Rachel Levy (MAA  Mathematical Association of America), Javier Rojo (Oregon State)Mathematical Modeling (MM) now has increased visibility in the education system and in the public domain. It appears as a content standard for high school mathematics and a mathematical practice standard across the K12 curriculum (Common Core Standards; and other states’ standards in mathematics education). Job opportunities are increasing in business, industry and government for those trained in the mathematical sciences. Quantitative reasoning is foundational for civic engagement and decisionmaking for addressing complex social, economic, and technological issues. Therefore, we must take action to support and sustain a significant increase in the teaching and learning of mathematical modeling from Kindergarten through Graduate School.
Mathematical modeling is an iterative process by which mathematical concepts and structures are used to analyze or gain qualitative and quantitative understanding of real world situations. Through modeling students can make genuine mathematical choices and decisions that take into consideration relevant contexts and experiences.
Mathematical modeling can be a vehicle to accomplish multiple pedagogical and mathematical goals. Modeling can be used to introduce new material, solidify student understanding of previously learned concepts, connect the world to the classroom, make concrete the usefulness (maybe even the advantages) of being mathematically proficient, and provide a rich context to promote awareness of issues of equity, sociopolitical injustices, and cultural relevance in mathematics.
A critical issue in math education is that although mathematical modeling is part of the K12 curriculum, the great majority of teachers have little experience with mathematical modeling as learners of mathematics or in their teacher preparation. In some cases, mathematics teacher educators have limited experience with mathematical modeling while being largely responsible for preparing future teachers.
Currently, the knowledge in teaching and learning MM is underdeveloped and underexplored. Very few MM resources seem to reach the K16 classrooms. Collective efforts to build a cohesive curriculum in MM and exploration of effective teaching practices based on research are necessary to make mathematical modeling accessible to teacher educators, teachers and students.
At the undergraduate level, mathematical modeling has traditionally been reserved for university courses for students in STEM majors beyond their sophomore year. Many of these courses introduce models but limit the students’ experience to using models that were developed by others rather than giving students the opportunity to generate their own models as is common in everyday life, in modeling competitions and in industry.
The CIME workshop on MM will bring together mathematicians, teacher educators, K12 teachers, faculty and people in STEM disciplines. As partners we can address ways to realize mathematical modeling in the K12 classrooms, teacher preparation, and lower and upper division coursework at universities. The content and pedagogy associated with teaching mathematical modeling needs special attention due to the nature of modeling as a process and as a body of content knowledge.Updated on Jan 28, 2019 11:09 AM PST 
Derived algebraic geometry and its applications
Organizers: Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), LEAD Nick Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Brooke Shipley (University of Illinois at Chicago)This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.
Updated on Sep 06, 2018 04:01 PM PDT 
Hot Topics: Recent progress in Langlands Program
Organizers: Mark Kisin (Harvard University), Elena Mantovan (California Institute of Technology), LEAD Xinwen Zhu (California Institute of Technology)The purpose of the workshop is to explain Vincent Lafforgue's ground breaking work, constructing the automorphic to Galois direction of the Langlands correspondence for function fields. There will also be a number of talks on more recent developments and related results.
Updated on Feb 01, 2019 12:11 PM PST 
2019 Spring Opportunities Workshop
Organizers: Brianna Donaldson (AIM  American Institute of Mathematics), Leslie Hogben, Michael Young (Iowa State University)GOAL: To highlight careers and opportunities in the mathematical sciences, and to prepare women
and underrepresented minorities for work in academia, industry, and government laboratories.Updated on Feb 14, 2019 03:33 PM PST 
Recent Progress in Moduli Theory
Organizers: Lucia Caporaso (Roma Tre University), LEAD Sándor Kovács (University of Washington), Martin Olsson (University of California, Berkeley)This workshop will be focused on presenting the latest developments in moduli theory, including (but not restricted to) recent advances in compactifications of moduli spaces of higher dimensional varieties, the birational geometry of moduli spaces, abstract methods including stacks, stability criteria, and applications in other disciplines.Updated on Sep 06, 2018 04:06 PM PDT 
Improving the Preparation of Graduate Students to Teach Undergraduate Mathematics
Organizers: Jack Bookman (Duke University), Shandy Hauk (WestEd), LEAD Dave Kung (St. Mary's College of Maryland), LEAD Natasha Speer (University of Maine)Is your department interested in helping graduate students learn to teach? Perhaps your department is considering starting a teachingfocused professional development program. Or maybe your department has a program but is interested in updating and enhancing it.
Many departments now offer presemester orientations, semesterlong seminars, and other opportunities for graduate students who are new to teaching so they will be wellequipped to provide highquality instruction to undergraduates. The purpose of this workshop is to support faculty from departments that are considering starting a teachingfocused professional development program or, for departments that have a program, to learn ways to improve it.
Updated on Feb 11, 2019 04:25 PM PST 
Connections for Women: Holomorphic Differentials in Mathematics and Physics
Organizers: Laura Fredrickson (Stanford University), Lotte Hollands (HeriotWatt University, Riccarton Campus), LEAD Qiongling Li (Chern Institute of Mathematics), Anna Wienhard (RuprechtKarlsUniversität Heidelberg), Grace Work (University of Illinois at UrbanaChampaign)This twoday workshop will consist of various talks given by prominent female mathematicians on topics of new developments in the role of holomorphic differentials on Riemann surfaces. These will be appropriate for graduate students, postdocs, and researchers in areas related to the program.
This workshop is open to all mathematicians.Updated on May 10, 2018 09:01 AM PDT 
Introductory Workshop: Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anna Wienhard (RuprechtKarlsUniversität Heidelberg)Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In this introductory workshop, we will bring junior and senior researchers from this diverse range of subjects together in order to explore common themes and unexpected connections.
Updated on Feb 05, 2019 12:03 PM PST 
Connections for Women: Microlocal Analysis
Organizers: Tanya Christiansen (University of Missouri), LEAD Raluca Felea (Rochester Institute of Technology)This workshop will provide a gentle introduction to a selection of applications of microlocal analysis. These may be drawn from among geometric microlocal analysis, inverse problems, scattering theory, hyperbolic dynamical systems, quantum chaos and relativity. The workshop will also provide a panel discussion, a poster session and an introduction/research session.
This workshop is open to all mathematicians.
Updated on Oct 22, 2018 11:23 AM PDT 
Introductory Workshop: Microlocal Analysis
Organizers: Pierre Albin (University of Illinois at UrbanaChampaign), LEAD Raluca Felea (Rochester Institute of Technology), Andras Vasy (Stanford University)Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This workshop will provide a comprehensive introduction to the field for postdocs and graduate students as well as specialists outside the field, building up from standard facts about the Fourier transform, distributions and basic functional analysis.
Updated on Sep 24, 2018 01:43 PM PDT 
Recent developments in microlocal analysis
Organizers: LEAD Pierre Albin (University of Illinois at UrbanaChampaign), Nalini Anantharaman (Université de Strasbourg), Colin Guillarmou (Université de Paris XI (ParisSud))Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory, hyperbolic dynamical systems, probability… As this description shows microlocal analysis has become a very broad area. Due to its breadth, it is a challenge for researchers to be aware of what is happening in other parts of the field, and the impact this may have in their own research area. The purpose of this workshop is thus to bring together researchers from different parts of microlocal analysis and its applications to facilitate the transfer of new ideas.
Updated on May 08, 2018 03:21 PM PDT 
Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at UrbanaChampaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anton Zorich (Institut de Mathematiques de Jussieu)Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukayatype categories, links to quantum integrable systems, or the physically derived construction of socalled spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special  Hitchin or higher Teichmuller  components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).
It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our workshop will be of interest to those working in many different fields, including lowdimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).
Updated on May 14, 2018 02:00 PM PDT 
Connections for Women: Quantum Symmetries
Organizers: Emily Peters (Loyola University), LEAD Chelsea Walton (University of Illinois at UrbanaChampaign)This workshop will feature several talks by experts, along with numerous 5minute presentations by junior mathematicians, on topics related to Quantum Symmetry. Such topics will include tensor categories, subfactors, Hopf algebras, topological quantum field theory and more. There will also be a panel discussion on professional development. The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.
Updated on Mar 26, 2018 12:18 PM PDT 
Introductory Workshop: Quantum Symmetries
Organizers: Vaughan Jones (Vanderbilt University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), LEAD Noah Snyder (Indiana University)This workshop will consist of introductory minicourses on key topics in Quantum Symmetry: fusion categories, modular tensor categories, Hopf algebras, subfactors and planar algebras, topological field theories, conformal nets, and topological phases of matter. These minicourses will be introductory and are aimed at giving semester participants exposure to the main ideas of subfields other than their own.
Updated on Apr 09, 2018 02:20 PM PDT 
Connections for Women: Higher Categories and Categorification
Organizers: Emily Riehl (Johns Hopkins University), LEAD Marcy Robertson (University of Melbourne)This twoday workshop will survey notable developments in the foundations and applications of higher category theory. It will consist of two minicourses given by emerging female leaders in the subject: Claudia Scheimbauer and Nathalie Wahl. This will be paired with a problem sessions lead by selected "TA's", themselves experts in higher structures. Each lecture series will be tailored to a diverse audience, accessible to graduate students and nonexpert researchers with some background in homological algebra.
The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.
Updated on Sep 14, 2018 02:07 PM PDT 
Introductory Workshop: Higher Categories and Categorification
Organizers: LEAD David Ayala (Montana State University), Emily Riehl (Johns Hopkins University), Christopher SchommerPries (University of Notre Dame), Peter Teichner (MaxPlanckInstitut für Mathematik)This workshop will survey notable developments and applications of higher category theory; it will be a venue for endusers to share their vision of how to apply the theory, as well as developers to share technical advancements. It will consist of 6 series of 3 lectures, each given by instrumental endusers & developers of higher category theory, together with a few questionanswer sessions. Each lecture series will be tailored to a diverse audience, accessible to graduate students and nonexpert researchers with some background in homological also algebra. The content of these lecture series will concern the following topics.
 Ktheory: categorification, noncommutative motives, trace methods;
 TQFT: functorial field theories, factorization homology.
 Parametrized higher category theory: stratifications, equivariant homotopy theory, operads, deformation theory and Koszul duality.
 Synthetic higher category theory: modelindependent characterizations, cosmoi.
Updated on Sep 14, 2018 02:08 PM PDT 
Tensor categories and topological quantum field theories
Organizers: Scott Morrison (Australian National University), Eric Rowell (Texas A & M University), LEAD Claudia Scheimbauer (Norwegian University of Science and Technology (NTNU)), Christopher SchommerPries (University of Notre Dame)The workshop will concern the latest developments in the mathematical study of quantum field theories. The focus will be on the interplay among topics such as higher category theory, as illustrated by the cobordism hypothesis, conformal field theory, tensor categories describing the quantum symmetries, and the relation to topological phases of matter.
Updated on Jul 03, 2018 04:02 PM PDT 
(∞, n)categories,factorization homology, and algebraic Ktheory
Organizers: LEAD Clark Barwick (University of Edinburgh), David Gepner (University of Melbourne), David Nadler (University of California, Berkeley), Marcy Robertson (University of Melbourne)This workshop will focus on recent developments in factorization homology, parametrized homotopy theory, and algebraic Ktheory. These seemingly disparate topics are unified by a common methodology, which leverages universal properties and unforeseen descent by way of higher category theory. Furthermore, they enjoy powerful and complementary roles in application to the cyclotomic trace. This workshop will be a venue for experts in these areas to present new results, make substantive connections across fields, and suggest and contextualize outstanding questions and problems. It will consist of 9 speakers, each delivering a 1hour morning talk and a 1hour afternoon talk, in addition to a session reserved for drawing attention to an assortment of outstanding problems.
Updated on Jun 25, 2018 10:56 AM PDT 
Connections for Women: Random and Arithmetic Structures in Topology
Organizers: LEAD Ursula Hamenstädt (Rheinische FriedrichWilhelmsUniversität Bonn), LEAD Fanny Kassel (Institut des Hautes Études Scientifiques (IHES))This twoday workshop will consist of various talks given by prominent female mathematicians in the field. These will be appropriate for graduate students, postdocs, and researchers in areas related to the program. The workshop will also include a professional development session.
This workshop is open to all mathematicians.
Updated on Jun 12, 2018 09:17 AM PDT

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