
Workshop Critical Issues in Mathematics Education 2019: Mathematical Modeling in K16: Community and Cultural Context
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 10, 2019 10:47 AM PST 
Summer Graduate School Commutative Algebra and its Interaction with Algebraic Geometry
Organizers: Craig Huneke (University of Virginia), Sonja Mapes (University of Notre Dame), Juan Migliore (University of Notre Dame), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame)Linkage is a method for classifying ideals in local rings. Residual intersections is a generalization of linkage to the case where the two `linked' ideals need not have the same codimension. Residual intersections are ubiquitous: they play an important role in the study of blowups, branch and multiple point loci, secant varieties, and Gauss images; they appear naturally in intersection theory; and they have close connections with integral closures of ideals.
Commutative algebraists have long used the Frobenius or pth power map to study commutative rings containing a finite field. The theory of tight closure and test ideals has widespread applications to the study of symbolic powers and to BrianconSkoda type theorems for equicharacteristic rings.
Numerical conditions for the integral dependence of ideals and modules have a wealth of applications, not the least of which is in equisingularity theory. There is a long history of generalized criteria for integral dependence of ideals and modules based on variants of the HilbertSamuel and the BuchsbaumRim multiplicity that still require some remnants of finite length assumptions.
The Rees ring and the special fiber ring of an ideal arise in the process of blowing up a variety along a subvariety. Rees rings and special fiber rings also describe, respectively, the graphs and the images of rational maps between projective spaces. A difficult open problem in commutative algebra, algebraic geometry, elimination theory, and geometric modeling is to determine explicitly the equations defining graphs and images of rational maps.
The school will consist of the following four courses with exercise sessions plus a Macaulay2 workshop
 Linkage and residual intersections
 Characteristic p methods and applications
 Blowup algebras
 Multiplicity theory
Updated on Aug 09, 2018 12:27 PM PDT 
Summer Graduate School Random and arithmetic structures in topology
Organizers: LEAD Alexander Furman (University of Illinois at Chicago), Tsachik Gelander (Weizmann Institute of Science)The study of locally symmetric manifolds, such as closed hyperbolic manifolds, involves geometry of the corresponding symmetric space, topology of towers of its finite covers, and numbertheoretic aspects that are relevant to possible constructions.The workshop will provide an introduction to these and closely related topics such as lattices, invariant random subgroups, and homological methods.Updated on Apr 20, 2018 03:02 PM PDT 
Workshop 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 Dec 03, 2018 08:51 AM PST 
Summer Graduate School Representation stability
Organizers: Thomas Church (Stanford University), LEAD Andrew Snowden (University of Michigan), Jenny Wilson (Stanford University)This summer school will give an introduction to representation stability, the study of algebraic structural properties and stability phenomena exhibited by sequences of representations of finite or classical groups  including sequences arising in connection to hyperplane arrangements, configuration spaces, mapping class groups, arithmetic groups, classical representation theory, Deligne categories, and twisted commutative algebras. Representation stability incorporates tools from commutative algebra, category theory, representation theory, algebraic combinatorics, algebraic geometry, and algebraic topology. This workshop will assume minimal prerequisites, and students in varied disciplines are encouraged to apply.
Updated on Aug 03, 2018 11:17 AM PDT 
Summer Graduate School Séminaire de Mathématiques Supérieures 2019: Current trends in Symplectic Topology
Organizers: Octav Cornea (Université de Montréal), Yakov Eliashberg (Stanford University), Michael Hutchings (University of California, Berkeley), Egor Shelukhin (Université de Montréal)Symplectic topology is a fast developing branch of geometry that has seen phenomenal growth in the last twenty years. This two weeks long summer school, organized in the setting of the Séminaire de Mathématiques Supérieures, intends to survey some of the key directions of development in the subject today thus covering: advances in homological mirror symmetry; applications to hamiltonian dynamics; persistent homology phenomena; implications of flexibility and the dichotomy flexibility/rigidity; legendrian contact homology; embedded contact homology and fourdimensional holomorphic techniques and others. With the collaboration of many of the top researchers in the field today, the school intends to serve as an introduction and guideline to students and young researchers who are interested in accessing this diverse subject.
Updated on Dec 10, 2018 04:21 PM PST 
Summer Graduate School Geometric Group Theory
Organizers: LEAD Rita Jiménez Rolland (Instituto de Matematicás, UNAMOaxaca), LEAD Pierre Py (Instituto de Matematicás, UNAMCiudad Universitaria)Geometric group theory studies discrete groups by understanding the connections between algebraic properties of these groups and topological and geometric properties of the spaces on which they act. The aim of this summer school is to introduce graduate students to specific central topics and recent developments in geometric group theory. The school will also include students presentations to give the participants an opportunity to practice their speaking skills in mathematics. Finally, we hope that this meeting will help connect Latin American students with their American and Canadian counterparts in an environment that encourages discussion and collaboration.
Updated on Aug 06, 2018 11:13 AM PDT 
Summer Graduate School Polynomial Method
Organizers: Adam Sheffer (Bernard M. Baruch College, CUNY), LEAD Joshua Zahl (University of British Columbia)In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques. In this summer school, we will discuss these new techniques as well as some exciting recent developments.
Updated on Nov 06, 2018 10:39 AM PST 
Summer Graduate School Recent topics on wellposedness and stability of incompressible fluid and related topics
Organizers: LEAD Yoshikazu Giga (University of Tokyo), Maria Schonbek (University of California, Santa Cruz), Tsuyoshi Yoneda (University of Tokyo)The purpose of the workshop is to introduce graduate students to fundamental results on the NavierStokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.
Updated on Jan 10, 2019 09:13 AM PST 
Summer Graduate School Toric Varieties
Organizers: David Cox (Amherst College), Henry Schenck (Iowa State University)Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.
Updated on Sep 21, 2018 04:02 PM PDT 
Summer Graduate School Mathematics of Machine Learning
Organizers: Sebastien Bubeck (Microsoft Research), Anna Karlin (University of Washington), Adith Swaminathan (Microsoft Research)Learning theory is a rich field at the intersection of statistics, probability, computer science, and optimization. Over the last decades the statistical learning approach has been successfully applied to many problems of great interest, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. These impressive successes relied crucially on the mathematical foundation of statistical learning.
Recently, deep neural networks have demonstrated stunning empirical results across many applications like vision, natural language processing, and reinforcement learning. The field is now booming with new mathematical problems, and in particular, the challenge of providing theoretical foundations for deep learning techniques is still largely open. On the other hand, learning theory already has a rich history, with many beautiful connections to various areas of mathematics (e.g., probability theory, high dimensional geometry, game theory). The purpose of the summer school is to introduce graduate students (and advanced undergraduates) to these foundational results, as well as to expose them to the new and exciting modern challenges that arise in deep learning and reinforcement learning.
Updated on Nov 30, 2018 06:41 PM PST 
Summer Graduate School HPrinciple
Organizers: LEAD Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)This two week summer school will introduce graduate students to the theory of hprinciples. After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, fluid dynamics, and foliation theory.
Updated on Sep 21, 2018 04:02 PM PDT 
Summer Graduate School Séminaire de Mathématiques Supérieures 2020: Discrete Probability, Physics and Algorithms
Organizers: Gerard Ben Arous, Alexander Fribergh (University of Montreal), Lea Popovic (Concordia University)Created on Jan 08, 2019 03:20 PM PST

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