MAMLS @ Harvard

May 9-10, 2009

A meeting on the intersections of logic and mathematics

The theme of the meeting is logic and its intersections with other branches of mathematics. Special sessions will showcase the work of junior logicians in the Boston area. On Saturday, May 9, there will be a conversation and audience Q&A with Barry Mazur, Bjorn Poonen and Carol Wood on logic and number theory. This will be followed by an informal reception and buffet dinner, to which all participants and their guests are invited.
Poster [PDF]
Place: Science Center 507, Harvard University, One Oxford Street, Cambridge, MA 02138
Dates: May 9-10, 2009
Organizer: Rehana Patel, Harvard University
Local Committee: Cameron Freer, Katherine Körner, Mia Minnes
Brooke Andersen (Framingham State College)Strong notions of reducibility
Cameron Freer (MIT) Computable de Finetti measures
Akihiro Kanamori (Boston University) Mathematical knowledge: motley and complexities of proof
Maryanthe Malliaris(UC Berkeley) Persistence and regularity in unstable theories
Barry Mazur (Harvard University) A conversation on logic and number theory (with Bjorn Poonen and Carol Wood)
Mia Minnes (MIT) Christol's theorem: surprising connections between automaticity, algebraicity, and morphic sequences
Andreea Nicoara (U Penn) Non-Noetherianity of the Denjoy-Carleman quasianalytic rings
Pedro Poitevin (Salem State University) Ranges of positive contractive projections in Nakano spaces
Bjorn Poonen (MIT) A sampler of undecidable problems + A conversation on logic and number theory (with Barry Mazur and Carol Wood)
Benjamin Rossman (MIT) k/4 variables are not enough for k-clique
Gerald Sacks (Harvard University) Models of long sentences
Maya Saran (UI Urbana-Champaign) A result on sigma-ideals of compact sets
Eric Wofsey (Harvard University) Noncommutative set theory
Carol Wood (Wesleyan University) A conversation on logic and number theory (with Barry Mazur and Bjorn Poonen)

Abstracts to the talks follow below

Schedule: All talks are in Science Center 507. Breakfast, coffee and reception in the 4th floor common room of the Science Center. To get to SC 507 take the elevator to the 4th floor and follow the signs.
8:45-9:15   Breakfast
9:15-9:30   Welcome & Announcements
9:30-10:30  Gerald Sacks
10:30-11:00 Coffee
11:00-11:25 Cameron Freer
11:30-11:55 Brooke Andersen
11:55-2:00  Lunch
2:00-3:00   Maryanthe Malliaris
3:00-3:30   Coffee
3:30-3:55   Ben Rossman
4:00-4:25   Mia Minnes
4:40-5:40   Barry Mazur, Bjorn Poonen, Carol Wood

5:40 onwards: Very informal reception and buffet dinner
9:00-9:30   Breakfast
9:30-10:30  Bjorn Poonen
10:30-11:00 Coffee
11:00-12:00 Andreea Nicoara
12:00-2:00  Lunch
2:00-2:25   Pedro Poitevin
2:30-2:55   Maya Saran
3:00-3:25   Eric Wofsey
3:30-4:00   Coffee
4:00-5:00   Akihiro Kanamori

Registration: The meeting is free and open to all. There is no formal registration, but if you do plan to attend, please email Rehana Patel at
Sponsors: The National Science Foundation through the Mid Atlantic Mathematical Logic Seminar (MAMLS), Harvard Mathematics Department, MIT Mathematics Department.
Support: MAMLS reimburses all out-of-town student participants at its conferences a flat amount of $50 for expenses. This can be arranged at the meeting without prior application. Additional support is available for students and junior researchers coming from outside the Boston area. Please send individual requests to Rehana Patel,, including your name, affiliation and an estimate of expenses. Applications will be considered on a rolling basis. Women and members of other groups traditionally under-represented in mathematics are especially encouraged to apply.
Accommodation: A block of rooms has been reserved for conference participants at the Sheraton Commander Hotel, a few minutes walk from the Harvard Science Center. The conference rate for rooms is $179 per night plus taxes. Parking is available at a special rate of $15 per day. These rates are guaranteed until May 1, 2009 (extended deadline), after which they will be subject to room availability. To make a reservation, start here.

Harvard Square Hotel
110 Mt Auburn St
MA 02138
Inn at Harvard
1201 Massachusetts Av
MA 02138
Gateway Inn
211 Concord Turnpike
MA 02140
The Friendly Inn
1673 Cambridge St
MA 02138
The Irving House
24 Irving St
MA 02138
Mary Prentiss Inn
6 Prentiss St
MA 02138

Travel information: Directions to the department.

Brooke Andersen: Strong notions of reducibility
Marcia Groszek and Rebecca Weber studied strengthenings of Turing reducibility defined by bounding conditions. I will survey their work and concentrate on a reducibility that is total on all computably enumerable oracles.
Bio: Brooke Andersen received her Ph.D. under the direction of Marcia Groszek at Dartmouth College in June 2008. For her thesis she compared strong notions of reducibility using complete sets. This past year she has been an Assistant Professor at Framingham State College and in January of 2010 she will be moving to Assumption College in Worcester, MA.
Cameron Freer: Computable de Finetti measures
We prove a uniformly computable version of de Finetti's theorem. The classical result states that an exchangeable sequence of real random variables is a mixture of independent and identically distributed (i.i.d.) sequences of random variables. Moreover, there is a measure-valued random variable, called the directing random measure, conditioned on which the random sequence is i.i.d. The distribution of the directing random measure is unique and is called the de Finetti measure. We show that computable exchangeable sequences of real random variables have computable de Finetti measures. (This is joint work with Daniel Roy.)
Bio: Cameron Freer is an Instructor of Pure Mathematics at MIT. He completed his PhD at Harvard in 2008 under the direction of Gerald Sacks.
Akihiro Kanamori: Mathematical knowledge: motley and complexities of proof
I describe mathematical knowledge as invested in the motley and complexities of proof, starting with an example in set theory and then surveying the contemporary mathematical landscape.
Bio: Akihiro Kanamori is Professor of Mathematics at Boston University. His interests are in set theory: research in large cardinals and consistency results, and the history and philosophy of set theory as embedded in analytic philosophy and its history. He is the author of The Higher Infinite (Spring-Verlag 1994), which has become the standard graduate text for large cardinals.
Maryanthe Malliaris: Persistence and regularity in unstable theories
Motivated in part by a question of Keisler about saturation of regular ultrapowers, we develop a framework which allows us to relate model-theoretic complexity to graph-theoretic notions of structure and randomness, notably Szemeredi regularity.
Bio: Maryanthe Malliaris is finishing her Ph.D. under the supervision of Thomas Scanlon at U.C. Berkeley. In the fall she will begin a Dickson Instructorship at the University of Chicago.
Barry Mazur: A conversation on logic and number theory (with Bjorn Poonen and Carol Wood)
Bio: Barry Mazur is Gerhard Gade University Professor of Mathematics at Harvard University.
Mia Minnes: Christol's theorem: surprising connections between automaticity, algebraicity, and morphic sequences
We will discuss Christol's beautiful theorem which lies at the crossroads of several disparate subjects. In particular, we will provide the necessary definitions to understand the theorem statement and, time permitting, outline the flavour of its proof. We will conclude with current attempts to extend Christol's theorem and ideas for applications.
Bio: Mia Minnes got her PhD from Cornell in 2008 under Anil Nerode. Her thesis proved results about automatic structures, answering questions about their complexity and applications. This is her first year as a CLE Moore Instructor at MIT. She will begin an SE Warschawski Assistant Professorship at UC San Diego in July of 2010
Andreea Nicoara: non-Noetherianity of the Denjoy-Carleman quasianalytic rings
The Denjoy-Carleman quasianalytic classes are subrings of the ring of smooth functions on which the Taylor morphism is injective, i.e. a function with zero derivatives up to infinite order is the zero function. Usually studied by analysts, these classes also have fascinating algebraic characteristics including that they fail to possess the Weierstrass Division Property. As a result, the standard inductive argument used for holomorphic and real-analytic functions to prove Noetherianity cannot be carried out. Whether these Denjoy-Carleman classes are Noetherian or non- Noetherian rings has thus been an open problem since 1976. I will discuss joint work with Liat Kessler (MIT) that settles this question using a modification of a Zariski structure satisfying quantifier elimination.
Bio: Andreea Nicoara is an Assistant Professor at the University of Pennsylvania. Previously, she held a Benjamin Peirce Assistant Professorship at Harvard University. She works at the intersection of several complex variables with algebraic geometry over non-Noetherian rings. More recently, she has been applying model theory to algebraic problems that arise in this work.
Pedro Poitevin: Ranges of positive contractive projections in Nakano spaces
Nakano spaces are generalizations of Lp-spaces in which the parameter p is allowed to vary randomly with the underlying measure space. We will characterize the possible ranges of positive contractive projections in Nakano spaces and discuss the model-theoretic significance of this characterization.
Bio: Pedro Poitevin did his graduate work under Ward Henson at the University of Illinois at Urbana-Champaign and is currently Assistant Professor at Salem State College. He is interested in continuous model theory of structures in functional analysis, particularly Banach lattices.
Bjorn Poonen: A sampler of undecidable problems
I will present a selection of problems from group theory, topology, number theory, and algebraic geometry that have been proved to be undecidable, and also present a few problems whose decidability status is not yet known.
A conversation on logic and number theory (with Barry Mazur and Carol Wood)
Bio: Poonen has a background in number theory and algebraic geometry, but occasionally works also on applications of these subjects to problems originating in logic. He has edited two books and authored about 80 research articles on a wide variety of mathematical topics. He is the founding managing editor of Algebra and Number Theory, a journal published by the nonprofit organization Mathematics Sciences Publishers.
Benjamin Rossman: k/4 variables are not enough for k-clique
We show that the k/4-variable fragment of first-order logic cannot define the class of finite ordered graphs which contain a k-clique. It was previously unknown whether 3 variables suffice to express every first-order property of finite ordered graphs.
Bio: Ben Rossman is a graduate student in theoretical computer science at MIT.
Gerald Sacks: Models of long sentences
Bio: Gerald Sacks is Professor of Mathematical Logic at Harvard University.
Maya Saran: A result on sigma-ideals of compact sets
For E a compact metric space, the space of its compact subsets, K(E), is itself compact metric. We consider sigma-ideals of compact sets, i.e., subsets of K(E) closed under the taking of subsets and countable (compact) unions. Such sigma-ideals typically arise out of various notions of smallness; their descriptive-set-theoretic study is well established. Solecki has proved a representation theorem for a broad natural class of sigma-ideals of compact sets. I will give the background, state his result, and present a theorem that refines it.
Bio: Maya Saran is finishing her PhD under Slawomir Solecki at the University of Illinois at Urbana-Champaign. Her research in descriptive set theory is on sigma-ideals of compact sets.
Eric Wofsey: Noncommutative set theory
By Gelfand duality, commutative unital C*-algebras are dual to compact Hausdorff spaces. Noncommutative C*-algebras can thus be thought of as the algebras of functions on some sort of "noncommutative spaces". When these spaces are taken to be geometric in nature, this is the starting point of the field of noncommutative geometry. However, if instead we take more set-theoretic spaces, we get what might be called "noncommutative set theory"? In particular, there is a natural non-commutative version of the Stone-Cech remainder beta omega-omega and many questions and results about the combinatorics of subsets of omega modulo finite sets have noncommutative analogs.
Bio: Eric Wofsey is a first-year grad student at Harvard University. He did some work in set theory as an undergraduate, but will probably now be specializing in algebraic topology.
Carol Wood: A conversation on logic and number theory (with Barry Mazur and Bjorn Poonen)
Bio: Carol Wood is Edward Burr Van Vleck Professor of Mathematics at Wesleyan University. She is a model theorist who admires applications of model theory to number theory and geometry, even ones she cannot quite understand.