# RTG in Mathematical Logic

Funded by NSF grants DMS-1044448 (Caltech), DMS-1044150 (UC-Irvine), DMS-1044604 (UCLA).

Mathematical Logic has a rich and distinguished history in Southern California. The National Science Foundation in 2011 recognized the strength of the Southern California Logic Group with the award of a 5 year RTG grant, joint among Caltech, UC-Irvine, and UCLA. The goal of the grant is to strengthen the training of students and postdoctoral fellows in Mathematical Logic, and in Mathematics in general, and to increase the number of US citizens and residents who pursue careers in these fields.

This page lists the programs, events, and fellowships supported through the RTG, with links to additional information when available. Click on the checkboxes to select the levels, campuses, and years shown.

## Levels shown: K-12 Undergraduate Graduate Postdoctoral Campuses shown: Caltech UC-Irvine UCLA Years shown: 2017-18 2016-17 2015-16 2014-15 2013-14 2012-13 2011-12

An inter-campus conference was held at UC-Irvine in March 2018, gathering group members from the three campuses and several RTG alumni.

A lunch seminar series for undergraduate students was organized at UC-Irvine in 2017-18. Monthly seminar talks are given by invited speakers selected for their ability to convey complex mathematical ideas in a clear simple fashion, and for their talent in communicating the beauty of mathematics. The goal of the talks is to introduce students to topics not normally covered in the undergraduate curriculum, and to fuel their interest in Mathematics.

The RTG's K-12 outreach supports the UC-Irvine Math Circle. The math circle is an enrichment program with classes for different age groups, from elementary to high school. Interested students from schools in Orange County can join the math circle by contacting theMath Circle Team, whose director is Alessandra Pantano. The program emphasizes reasoning and discovery. Activities are described on the program webpage http://www.math.uci.edu/~mathcircle.

The UC-Irvine Community Education Outreach (Math CEO) hosted math circle meetings for students from middle schools where the average family education is low. Every Wednesday after school students are transported to UC-Irvine to participate in math circles led by college students and faculty, and solve original, program-created, challending math problems. These mathematical experiences are designed to promote and build skills neessary to succeed in STEM careers, develop higher level thinking and persistence on hard tasks, and reinforce students' appreciation of mathematics.

Nam Trang was supported on a postdoctoral fellowship at UC-Irvine in Fall 2017 and Winter 2018.

Kirill Gura and Julian Ziegler-Hunts were awarded an RTG graduate fellowship for 2017-18 at UCLA. In addition Alex Mennen received a partial graduate fellowship from the RTG.

Joshua Frisch recieved a partial graduate fellowsip from the RTG at Caltech in 2017-18.

A graduate summer school on classification problems in ergodic theory was held at UC-Irvine in summer 2017. The graduate summer schools cover recent research in specific areas of logic. Participants read papers on current topics of research, lectures on these papers are given by faculty and postdocs, and there are problem sessions centered on recent results and open questions. Information about the 2017 graduate summer school is available at https://www.math.uci.edu/STsummerschool/.

A course on Transition to upper division Mathematics was given at UCLA during summer session 2017, with fellowships to help pay registration fees available for community college students who are transferring to UCLA, and freshmen admits with sufficient advance standing for upper division courses. The goal of the course is to prepare students for the transition from lower division and advanced placement courses to the more abstract and proof-based upper division courses in pure mathematics.

A lunch seminar series for undergraduate students was organized at UC-Irvine in 2016-17. Monthly seminar talks are given by invited speakers selected for their ability to convey complex mathematical ideas in a clear simple fashion, and for their talent in communicating the beauty of mathematics. The goal of the talks is to introduce students to topics not normally covered in the undergraduate curriculum, and to fuel their interest in Mathematics.

The RTG's K-12 outreach supports the UC-Irvine Math Circle. The math circle is an enrichment program with classes for different age groups, from elementary to high school. Interested students from schools in Orange County can join the math circle by contacting theMath Circle Team, whose director is Alessandra Pantano. The program emphasizes reasoning and discovery. Activities are described on the program webpage http://www.math.uci.edu/~mathcircle.

The UC-Irvine Community Education Outreach (Math CEO) hosted math circle meetings for students from middle schools where the average family education is low. Every Wednesday after school students are transported to UC-Irvine to participate in math circles led by college students and faculty, and solve original, program-created, challending math problems. These mathematical experiences are designed to promote and build skills neessary to succeed in STEM careers, develop higher level thinking and persistence on hard tasks, and reinforce students' appreciation of mathematics. A different STEM career is introduced to the middle-school students at every meeting.

Two STEM-focused campus visits to UC-Irvine were organized in May 2017 for students from the Math CEO middle-schools. These capstone trips to UC-Irvine labs supplement the Math CEO weekly meetings, showcasing the many applications of mathematics to other sciences, and giving the students a taste of college life, spending a day on campus together with their undergraduate mentors.

The UC-Irvine Math CEO program hosted two bilingual college workshops for parents of middle-school students. The goal of the workshops is to inform parents about pathways to college and financial aid available to academically talented low-income students. The programs have been tremendously successful, with parents overwhelmingly indicating that the workshops were effective in increasing their interest in college.

Nam Trang was supported on a postdoctoral fellowship in 2016-17 at UC-Irvine.

Spencer Unger was supported on a postdoctoral fellowship in 2016-17 at UCLA.

Joshua Frisch was awarded an RTG graduate fellowship for the academic year 2016-17 at Caltech.

Ryan Sullivant, Kameran Kolahi, Trevor White, and Garret Erving were awarded RTG graduate fellowships in 2016-17 at UC-Irvine.

Riley Thornton was awarded an RTG graduate fellowship for the academic year 2016-17 at UCLA.

A graduate summer school on singular cardinal combinatorics was held at UC-Irvine in summer 2016. The graduate summer schools cover recent research in specific areas of logic. Participants read papers on current topics of research, lectures on these papers are given by faculty and postdocs, and there are problem sessions centered on recent results and open questions. Information about the 2016 graduate summer school is available at http://www.math.cmu.edu/users/jcumming/summer_school/.

An undergraduate summer school in mathematical logic was held at UCLA in summer 2016. The goal of the summer school is to introduce future mathematicians to central results and techniques from mathematical logic. Undergraduates from any institution are eligible to apply. Courses are very intensive, and reach advanced graduate level material. At the same time they are designed to not require specific background in logic (they do require substantial background in mathematics and high mathematical sophistication). The courses given in 2016 were on cardinal arithmetic, forcing and independence in set theory, and o-minimality, variations, and applications. Further information is available at http://www.math.ucla.edu/~ineeman/Summer-old-2016/.

A course on Transition to upper division Mathematics was given at UCLA during summer session 2016, with fellowships to help pay registration fees available for community college students who are transferring to UCLA, and freshmen admits with sufficient advance standing for upper division courses. The goal of the course is to prepare students for the transition from lower division and advanced placement courses to the more abstract and proof-based upper division courses in pure mathematics.

Inter-campus conferences were held at UC-Irvine in Fall 2015, at Caltech in Winter 2016, and at UCLA in Spring 2016. Talks were given by graduate students and postdocs from the three RTG campuses, allowing them to present research results and practice their presentation skills in conference settings.

A lunch seminar series for undergraduate students was organized at UC-Irvine in 2015-16. Monthly seminar talks are given by invited speakers selected for their ability to convey complex mathematical ideas in a clear simple fashion, and for their talent in communicating the beauty of mathematics. The goal of the talks is to introduce students to topics not normally covered in the undergraduate curriculum, and to fuel their interest in Mathematics.

The RTG's K-12 outreach supports the UC-Irvine Math Circle. The math circle is an enrichment program with classes for different age groups, from elementary to high school. Interested students from schools in Orange County can join the math circle by contacting the Math Circle Team, whose director is Alessandra Pantano. The program emphasizes reasoning and discovery. Activities are described on the program webpage http://www.math.uci.edu/~mathcircle.

The Lathrop Middle School Math Circle outreach program at UC-Irvine was renamed Community Education Outreach (CEO) and expanded substantially. It hosted regular Math Circle meetings in two middle schools in Santa Ana, Lathrop Intermediate and Villa Fundamental, where approximately 100 middle school students work on innovative math curriculum with a large group of volunteers from UC-Irvine (including faculty, graduate students, alumni, and undergraduates majoring in math, biology, engineering, and education). In addition Math CEO organized events intended to inform students and parents in the middle schools about college life and pathways to college. These include bilingual evening workshops for parents at the middle schools, and day field trips for the students to science labs at UC-Irvine. The programs have been tremendously successful, with overwhelmingly positive feedback from the parents, students, and teachers. A list of Math CEO activities is available at https://www.math.uci.edu/mathceo/meetings.php.

Benjamin Siskind (UC-Berkeley graduate student) received support to attend the UC-Irvine conference on descriptive inner model theory and HOD mice.

Nam Trang was supported on a postdoctoral fellowship in Spring 2016 at UC-Irvine.

Ryan Sullivant was awarded an RTG graduate fellowship for the academic year 2015-16 at UC-Irvine.

Alex Mennen was awarded an RTG graduate fellowship for the academic year 2015-16 at UCLA.

Aaron Anderson participated in an REU at Caltech in summer 2016, working under the direction of Alexander Kechris.

A graduate summer school on forcing and large cardinals was held at UC-Irvine in summer 2015. The graduate summer schools cover recent research in specific areas of logic. Participants read papers on current topics of research, lectures on these papers are given by faculty and postdocs, and there are problem sessions centered on recent results and open questions. Information about the 2015 graduate summer school is available at https://gssst2015.wordpress.com/.

An undergraduate summer school in mathematical logic was held at UCLA in summer 2015. The goal of the summer school is to introduce future mathematicians to central results and techniques from mathematical logic. Undergraduates from any institution are eligible to apply. Courses are very intensive, and reach advanced graduate level material. At the same time they are designed to not require specific background in logic (they do require substantial background in mathematics and high mathematical sophistication). The courses given in 2015 were on first order logic and Gödel incompleteness, and determinacy. Further information is available at http://www.math.ucla.edu/~ineeman/Summer-old-2015/.

A course on Transition to upper division Mathematics was given at UCLA during summer session 2015, with fellowships to help pay registration fees available for community college students who are transferring to UCLA, and freshmen admits with sufficient advance standing for upper division courses. The goal of the course is to prepare students for the transition from lower division and advanced placement courses to the more abstract and proof-based upper division courses in pure mathematics.

An Opportunities in Mathematics workshop was held at UC-Irvine in April, 2015. The workshop aims to encourage middle stage undergraduate students to apply to graduate school in mathematics. The workshop included a plenary talk by Prof. Erika Camacho from Arizona State University, and panel discussions on graduate student life, careers in mathematics, REUs, and the graduate school application process. Information about the workshop is available at http://www.math.uci.edu/~mathoppworkshop/.

Inter-campus conferences were held at UCLA in Fall 2014, and at Caltech in Winter 2015. Talks were given by graduate students and postdocs from the three RTG campuses, allowing them to present research results and practice their presentation skills in conference settings.

A lunch seminar series for undergraduate students was organized at UC-Irvine in 2014-15. Monthly seminar talks are given by invited speakers selected for their ability to convey complex mathematical ideas in a clear simple fashion, and for their talent in communicating the beauty of mathematics. The goal of the talks is to introduce students to topics not normally covered in the undergraduate curriculum, and to fuel their interest in Mathematics.

The RTG's K-12 outreach supports the UC-Irvine Math Circle. The math circle is an enrichment program with classes for different age groups, from elementary to high school. Interested students from schools in Orange County can join the math circle by contacting the Math Circle Team, whose director is Alessandra Pantano. The program emphasizes reasoning and discovery. Activities are described on the program webpage http://www.math.uci.edu/~mathcircle. In addition to the program on campus at UC-Irvine, in 2014-15 the Math Circle organized meetings at Lathrop Intermediate School, and a visit to campus for the students and their parents, with a program in English and Spanish that included meetings with first generation college students, and outreach information on college applications and financial aid.

Garett Ervin (UC-Irvine graduate student) received travel support to visit Cornell University to work with Prof. Justin Moore.

Prof. Paul Larson of Miami University at Oxford, Ohio, was invited to UC-Irvine and gave a series of talks, on P-max forcing and on automorphisms of $P(\lambda)/Fin$ to graduate students.

Alexander McDonald was awarded an RTG graduate fellowship for the academic year 2014-15 at Caltech.

Geoff Galgon was awarded an RTG graduate fellowship for the academic year 2014-15 at UC-Irvine.

Thomas Gilton was awarded an RTG graduate fellowship for the academic year 2014-15 at UCLA.

Michael Wheeler participated in an REU at Caltech in summer 2015, working under the direction of Alexander Kechris.

An undergraduate summer school in mathematical logic was held at UCLA in summer 2014. The goal of the summer school is to introduce future mathematicians to central results and techniques from mathematical logic. Undergraduates from any institution are eligible to apply. Courses are very intensive, and reach advanced graduate level material. At the same time they are designed to not require specific background in logic (they do require substantial background in mathematics and high mathematical sophistication). The courses given in 2014 were on descriptive set theory, and forcing. Further information is available at http://www.math.ucla.edu/~ineeman/Summer-old-2014/.

A course on Transition to upper division Mathematics was given at UCLA during summer session 2014, with fellowships to help pay registration fees available for community college students who are transferring to UCLA, and freshmen admits with sufficient advance standing for upper division courses. The goal of the course is to prepare students for the transition from lower division and advanced placement courses to the more abstract and proof-based upper division courses in pure mathematics. The 2014 course webpage is at http://www.math.ucla.edu/~kouellet/95.1.141c/.

Inter-campus conferences were held at UCLA in Fall 2013, at Caltech in Winter 2014, and at UCI in Spring 2014. Talks were given by graduate students and postdocs from the three campuses, allowing them to present research results and practice their presentation skills in conference settings.

A lunch seminar series for undergraduate students was organized at UC-Irvine in 2013-14. Monthly seminar talks are given by invited speakers selected for their ability to convey complex mathematical ideas in a clear simple fashion, and for their talent in communicating the beauty of mathematics. The goal of the talks is to introduce students to topics not normally covered in the undergraduate curriculum, and to fuel their interest in Mathematics.

Jay Williams (Caltech postdoc) gave a general audience talk on set theory at an introductory undergraduate level, titled Buckets, balls, and the axiom of choice, in February 2014 at Pomona College, one of the Claremont Colleges concentrating on undergraduate education. The goal of this component of the RTG is to introduce students at colleges that primarily teach undergraduates to material in Mathematical logic.

The RTG's K-12 outreach supports the UC-Irvine Math Circle. The math circle is an enrichment program with classes for different age groups, from elementary to high school. Interested students from schools in Orange County can join the math circle by contacting the Math Circle Team, whose director is Alessandra Pantano. The program emphasizes reasoning and discovery. Activities are described on the program webpage http://www.math.uci.edu/~mathcircle.

Spencer Unger was awarded an RTG postdoctoral fellowship for the academic years 2013-14 through 2015-16 at UCLA.

William Chan was awarded an RTG graduate fellowship for the academic year 2013-14 at Caltech.

Garrett Ervin and Ryan Sullivant were awarded RTG graduate fellowships for the academic year 2013-14 at UC-Irvine.

Anton Bobkov and Assaf Shani were awarded RTG graduate fellowships for the academic year 2013-14 at UCLA.

Sam Holo participated in an REU at Caltech in summer 2014, working under the direction of Alexander Kechris.

A graduate summer school on large cardinals, inner models, and determinacy was held at UC-Irvine in summer 2013. The graduate summer schools cover recent research in specific areas of logic. Participants read papers on current topics of research, lectures on these papers are given by faculty and postdocs, and there are problem sessions centered on recent results and open questions. Information about the 2013 graduate summer school is available at http://www.math.uci.edu/~mzeman/RTG-2010/GSS-2013/gss-13.html.

An undergraduate summer school in mathematical logic was held at UCLA in summer 2013. The goal of the summer school is to introduce future mathematicians to central results and techniques from mathematical logic. Undergraduates from any institution are eligible to apply. Courses are very intensive, and reach advanced graduate level material. At the same time they are designed to not require specific background in logic (they do require substantial background in mathematics and high mathematical sophistication). The courses given in 2013 were on applied recursion theory, descriptive set theory, and forcing. Further information is available at http://www.math.ucla.edu/~ineeman/Summer-old-2013/.

A course on Transition to upper division Mathematics was given at UCLA during summer session 2013, with fellowships to help pay registration fees available for community college students who are transferring to UCLA. The goal of the course is to prepare students for the transition from lower division and advanced placement courses to the more abstract and proof-based upper division courses in pure mathematics. The 2013 course webpage is at http://www.math.ucla.edu/~kouellet/95.1.131c/.

Inter-campus conferences were held at Caltech in Fall 2012, at UCI in Winter 2013, and at UCLA in Spring 2013. Talks were given by graduate students and postdocs from the three campuses, allowing them to present research results and practice their presentation skills in conference settings.

A lunch seminar series for undergraduate students was organized at UC-Irvine in 2012-13. Monthly seminar talks are given by invited speakers selected for their ability to convey complex mathematical ideas in a clear simple fashion, and for their talent in communicating the beauty of mathematics. The goal of the talks is to introduce students to topics not normally covered in the undergraduate curriculum, and to fuel their interest in Mathematics.

Jay Williams (Caltech postdoc) gave a general audience talk on set theory at an introductory undergraduate level, titled An introduction to infinity, in March 2013 at Pasadena City College. Approximately 75 people attended. The goal of this component of the RTG is to introduce students at colleges that primarily teach undergraduates to material in Mathematical logic.

Mathematics day trips for high school students were organized at UC-Irvine throughout the academic year 2012-13. These day trips bring high school students to the UCI campus for a day of hands-on math activities, a panel discussion with undergraduate math majors, and a tour of the UCI campus. The hands-on math activities are designed to introduce students to advanced undergraduate level mathematics topics that are not similar to anything found in the standard high school curriculum. The topics covered in 2012-13 include game theory, machine learning, symmetric groups, and knot theory. Five classes visited during 2012-13, ranging in size from 28 to 49 students, from Santa Any Valley School, Godinez Fundamental High School, Woodbridge High School, Irvine High School, and Sage Hill High School.

Jay Williams was awarded an RTG postdoctoral fellowship for the academic years 2012-13 through 2014-15 at Caltech.

Trevor Wilson was awarded an RTG postdoctoral fellowship for the academic years 2012-13 and 2013-14 at UC-Irvine.

William Chan was awarded an RTG graduate fellowship for the academic year 2012-13 at Caltech.

Geoff Galgon was awarded an RTG graduate fellowship for the academic year 2012-13 at UC-Irvine.

John Susice was awarded an RTG graduate fellowship for the academic year 2012-13 at UCLA.

Alex Port participated in an REU at Caltech in summer 2013, working under the direction of Alexander Kechris.

A graduate summer school on large cardinals, inner models, and fine structure was held at UC-Irvine in summer 2012. The graduate summer schools cover recent research in specific areas of logic. Participants read papers on current topics of research, lectures on these papers are given by faculty and postdocs, and there are problem sessions centered on recent results and open questions. Information about the 2012 graduate summer school is available at http://www.math.uci.edu/~mzeman/RTG-2010/GSS-2012/gss-2012.html.

An undergraduate summer school in mathematical logic was held at UCLA in summer 2012. The goal of the summer school is to introduce future mathematicians to central results and techniques from mathematical logic. Undergraduates from any institution are eligible to apply. Courses are very intensive, and reach advanced graduate level material. At the same time they are designed to not require specific background in logic (they do require substantial background in mathematics and high mathematical sophistication). The courses given in 2012 were on first order logic and the Goedel incompleteness theorem, forcing and independence in set theory, and non-standard analysis. Further information is available at http://www.math.ucla.edu/~ineeman/Summer-old-2012/.

A course on Transition to upper division Mathematics was given at UCLA during summer session 2012, with fellowships to help pay registration fees available for community college students who are transferring to UCLA. The goal of the course is to prepare students for the transition from lower division and advanced placement courses to the more abstract and proof-based upper division courses in pure mathematics.

Inter-campus conferences were held at UC-Irvine in Fall 2011, at Caltech in Winter 2012, and at UCLA in Spring 2012. Talks were given by graduate students and postdocs from the three campuses, allowing them to present research results and practice their presentation skills in conference settings.

A lunch seminar series for undergraduate students was organized at UC-Irvine in 2011-12. Monthly seminar talks are given by invited speakers selected for their ability to convey complex mathematical ideas in a clear simple fashion, and for their talent in communicating the beauty of mathematics. The goal of the talks is to introduce students to topics not normally covered in the undergraduate curriculum, and to fuel their interest in Mathematics. The final, capstone, talk of the year was also open to a group of students and teachers from a local high-school.

Isaac Goldbring (a UCLA postdoc at the time) gave general audience talks at an introductory undergraduate level, on non-standard analysis, in Fall 2011 at Claremont McKenna College and at Loyola Marymount University. Approximately 85 people attended at Claremont McKenna, and 35 at Loyola. The goal of this component of the RTG is to introduce students at colleges that primarily teach undergraduates to material in Mathematical logic.

Mathematics day trips for high school students were organized at UC-Irvine throughout the academic year 2011-12. These day trips bring high school students to the UCI campus for a day of hands-on math activities, a panel discussion with undergraduate math majors, and a tour of the UCI campus. The hands-on math activities are designed to introduce students to advanced undergraduate level mathematics topics that are not similar to anything found in the standard high school curriculum. The topics covered in 2011-12 include game theory, machine learning, and properties of symmetric groups demonstrated through a card game that was invented by UC-Irvine graduate students Cynthia Northrup and Zac Faubion. Six visit days were held during 2011-12. Five were coordinated with specific high school classes, from Godinez High School, Woodbridge High School, Sage Hill School, and University High School, with attendance ranging between 35 and approximately 100 students. The sixth was not class specific but instead open to any interested local high-school students, with attendance of 18 participants.

Dima Sinapova was awarded an RTG postdoctoral fellowship for the academic year 2011-12 at UC-Irvine.

Garrett Ervin was awarded an RTG graduate fellowship for the academic year 2011-12 at UC-Irvine.

Anton Bobkov was awarded an RTG graduate fellowship for the academic year 2011-12 at UCLA.

Andrew Zucker participated in an REU at Caltech in summer 2012, working under the direction of Alexander Kechris.