Mathematics & Computer Science

Seminars and Colloquia

Logic Seminar

Monday, September 26, 2016

04:45 pm - 06:00 pm

Logic Seminar

Philip Scowcroft, Wes: " Abelian lattice-ordered groups with at most finitely many pairwise disjoint elements." Abstract : Conrads characterization (1960) of the lattice-ordered groups with at most finitely many pairwise disjoint elements yields model-completions for various theories of such groups. A corresponding Nullstellensatz, and various quantifier-elimination results, assume stronger forms when restricted to special groups in the class.

Exley Science Center Tower ESC 638

Monday, November 09, 2015

04:45 pm - 06:00 pm

Logic Seminar, Bill Calhoun (Bloomsburg University): "Triviality and lowness for K-reducibility and related reducibilities"

n 2 !, where K is prefix-free Kolmogorov complexity. The set A is low for K if KA(y) = K(y)+O(1) for y 2 2<!. These definitions seem quite different. K-triviality indicates that initial segments of A have the lowest possible complexity, while lowness for K indicates that A is too weak as an oracle to reduce the complexity of any string. The remarkable equivalence of the two definitions was shown by Nies [2]. Replacing prefix-free complexity by monotone complexity in the definition of K-trivial, we obtain the Km-trivial sets. Every K-trivial set is Km-trivial and all Turing degrees _ 00 contain a Km-trivial set [1]. Yet, not every Turing degree contains a Km-trivial set. We obtain a superset of the Km-trivial sets by defining A to be almost-K-trivial if there is a real number a such that K(A _ n) _+ aK(n). Every Km-trivial set is almost-K-trivial. However, the Turing degree of a computably dominated ML-random cannot contain any almost-K-trivial set. An interesting question is to determine which Turing degrees contain Km-trivial sets (or almost-K-trivial sets). Recently, this question has been considered for minimal Turing degrees. We also consider lowness for monotone and a priory complexity. References 1. Calhoun, W.C.: Triviality and minimality in the degrees of monotone complexity, Journal of Logic and Computation 22, 197-206 (2012). 2. Nies, Andre: Lowness properties and randomness, Advances in Mathematics 197, 274-305 (2005).

Exley Science Center (Tower)

Monday, November 02, 2015

04:45 pm - 05:00 pm

Logic Seminar, Philip Scowcroft (Wes): Infinitely generic Abelian lattice-ordered groups

Abstract: This talk will survey current knowledge of the infinitely generic Abelian lattice-ordered groups as well as the mysteries that remain.

Exley Science Center (Tower)

Monday, September 21, 2015

04:45 pm - 06:00 pm

CT Logic Seminar, Vincent Guingona (Wes): "A Local Characterization of VC-Minimality"

Abstract : ( Joint work with Uri Andrews ) This talk is in the intersection of computable model theory and neostability theory. I discuss VC-minimality, a model-theoretic notion of complexity for theories that generalizes o-minimality and is generalized by dp-minimality and NIP. Unlike o-minimality and dp-minimality, a priori , it is difficult to determine if a given theory is VC-minimal. In computability terms, the definition of VC-minimality, in its original form, is Sigma_1^1. However, my coauthor and I show that VC-minimality is, in fact, Pi^0_4-complete by giving a local characterization (for countable languages). This leads to a list of examples of theories whose VC-minimality is determined.

Exley Science Center (Tower)

Monday, September 14, 2015

04:45 pm - 05:45 pm

Logic Seminar, Reed Solomon (UConn): "Strong reducibilities, RT^1_3 and SRT^2_2"

Abstract: Various strong reductions between Pi^1_2 principles have been used in recent years to shed light on difficult problems in reverse mathematics. I will introduce some of these reductions and discuss their connection to reverse math. The main theorem of the talk is that RT^1_3 is not strongly computably reducible to SRT^2_2. This result is joint work with Damir Dzhafarov, Ludovic Patey and Linda Brown Westrick.

Monday, April 27, 2015

04:45 pm - 06:00 pm

Logic Seminar, Petr Glivicky (Charles University): 'Definability in linear fragments of Peano Arithmetic'

Abstract: In this talk, I will give an overview of recent results on linear arithmetics with main focus on definability in their models. Here, for a cardinal k, the k-linear arithmetic (LAk) is a full-induction arithmetical theory extending Presburger arithmetic by k non-standard scalars (= unary functions of multiplication by distinguished elements). The hierarchy of linear arithmetics lies between Presburger and Peano arithmetics and stretches from tame to wild. I will present a quantifier elimination result for LA1 and give a complete characterisation of definable sets in its models. On the other hand, I will construct an example of a model of LA2 (or any LAk with k at least 2) where multiplication is definable on a non-standard initial segment (and thus no similar quantifier elimination is possible). There is a close connection between models of linear arithmetics and certain discretely ordered modules (as each model of a linear arithmetic naturally corresponds to a discretely ordered module over the ordered ring generated by the scalars) which allows to construct wild (e.g. non-NIP) ordered modules. On the other hand, the quantifier elimination result for LA1 implies interesting properties of the structure of saturated models of Peano arithmetic.

ESC 638

Monday, March 30, 2015

04:45 pm - 06:00 pm

Logic Seminar, Reed Solomon (UConn): 'Revisiting EM and ADS'

Abstract: In this talk, I will present recent work by Ludovic Patey which simplifies and extends the proof that the Erdos-Moser principle (that every infinite tournament has an infinite transitive sub tournament) does not imply ADS (that every linear order contains either an infinite ascending sequence or an infinite descending sequence).

ESC 638

Tuesday, March 24, 2015

04:15 pm - 05:30 pm

Computer Science Seminar, Marc Liberatore (UMass): 'BitCoin: WTF is it, and is it really anonymous?'

Abstract: In this talk, we'll (re-)develop the BitCoin protocol step-by-step. We'll start with a simple centralized service for digital cash, and end up with a sketch of the distributed consensus system that we all love -- or love to hate. We will briefly survey the state of BitCoin and related systems, with a focus on how much privacy they really provide to their users. Then, we'll present the problem of mixing BitCoin to increase user privacy. We will see that centralized mix systems based on protocols like CoinJoin have the same problems found in centralized proxies for general communications, and more besides. We'll show that the Sybil attack is one such problem -- a critical one -- and present Xim, our distributed approach to Sybil-resistant matchmaking.(While this talk will be technical, you won't need a deep knowledge of cryptography or protocols to follow it. My goal is for undergraduate liberal arts majors with some math or computer science background to be comfortable in following along and in asking questions as they come up.)Marc Liberatore is a research scientist and occasional lecturer in the School of Computer Science at the University of Massachusetts Amherst, and the associate director of the Center for Forensics at UMass. Prior to his current appointment, he was a Mellon Fellow and Visiting Assistant Professor at Wesleyan University. His research interests include network, cellular, and filesystem forensics, anonymous communication systems, and peer-to-peer architectures.

ESC 638

Tuesday, March 24, 2015

04:15 pm - 05:30 pm

Computer Science Seminar, Marc Liberatore (UMass): 'BitCoin: WTF is it, and is it really anonymous?'

Abstract: In this talk, we'll (re-)develop the BitCoin protocol step-by-step. We'll start with a simple centralized service for digital cash, and end up with a sketch of the distributed consensus system that we all love -- or love to hate. We will briefly survey the state of BitCoin and related systems, with a focus on how much privacy they really provide to their users. Then, we'll present the problem of mixing BitCoin to increase user privacy. We will see that centralized mix systems based on protocols like CoinJoin have the same problems found in centralized proxies for general communications, and more besides. We'll show that the Sybil attack is one such problem -- a critical one -- and present Xim, our distributed approach to Sybil-resistant matchmaking. (While this talk will be technical, you won't need a deep knowledge of cryptography or protocols to follow it. My goal is for undergraduate liberal arts majors with some math or computer science background to be comfortable in following along and in asking questions as they come up.) Marc Liberatore is a research scientist and occasional lecturer in the School of Computer Science at the University of Massachusetts Amherst, and the associate director of the Center for Forensics at UMass. Prior to his current appointment, he was a Mellon Fellow and Visiting Assistant Professor at Wesleyan University. His research interests include network, cellular, and filesystem forensics, anonymous communication systems, and peer-to-peer architectures.

ESC 638

Monday, March 23, 2015

04:45 pm - 06:00 pm

Logic Seminar, Stephen Flood (UConn): 'Separating Decomposability and Tree- Decomposability'

Abstract: The theory of graph decompositions studies the infinite graphs that can be built using a sequence of irreducible graphs which are pasted together at complete subgraphs. In this theory, there are several combinatorial characterizations of the tree-decomposable graphs, but a combinatorial characterization of general decomposable graphs has proved elusive.In this talk, we approach this question from the perspective of mathematical logic. We show that there is indeed a difference between characterizing decomposable and tree-decomposable graphs. More precisely, we show that the index set of computable decomposable graphs is $\Pi^1_1$ hard and $\Sigma^1_2$ definable, whereas the index set of computable tree-decomposable graphs is $\Sigma^1_1$ definable.

ESC 638

Monday, November 17, 2014

04:45 pm - 06:00 pm

CT Logic Seminar, Linda Brown Westrick (UConn): 'Effective Dimension in Subshifts'

Abstract: A subshift is a subset of Cantor space that is both topologically closed and closed under the shift operation. Any element of a subshift can be viewed as a trajectory in a discrete dynamical system. One way a trajectory can be complicated is to have a large effective dimension. We consider the effective dimension spectrum of a subshift X, defined as {dim x : x in X}, where dim is the effective dimension. Most commonly, the dimension spectrum of X is [0,h(X)], where h(X) is the entropy of X. We give examples where the dimension spectrum does not follow this pattern, and discuss partial results and open questions related to the problem of characterizing the dimension spectra of subshifts. No prior knowledge about subshifts will be assumed.

ESC 638

Monday, November 10, 2014

04:45 pm - 06:00 pm

CT Logic Seminar, Gwyneth Harrison-Shermoen (Wes): 'Independence, via limits'

Abstract: Given a large model $M$ of some theory $T$, I will describe a method for lifting well-behaved notions of independence from the theories of substructures of $M$ to a reasonably well-behaved notion of independence in $M$. (In essence, we take the limit of the independence relations in the substructures.) The motivating example - two-sorted theories of infinite-dimensional vector spaces over an algebraically closed field and with a bilinear form - was worked out by N. Granger in his thesis. I will outline this example before launching into the more general framework.

ESC 638

Monday, October 27, 2014

04:45 pm - 06:00 pm

CT Logic Seminar, Cameron Hill (Wes): 'Some Remarks on Certain 0,1-Laws'

Abstract: I will begin by reminding everyone what a Fra\iss\e class is, and I will introduce a certain family of ultrafilters related to such a class. After that, I will review what is (usually) intended when one says that a Fra\iss\e class has a 0,1-law for first-order sentences. Finally, I will propose a method of indexing asymptotic distributions on a Fra\iss\e class by elements of a certain compact space, and I will discuss some results that can be proved using this method.

ESC 638

Monday, September 22, 2014

04:45 pm - 06:00 pm

CT Logic Seminar, Jim Schmerl (UConn): 'The Automorphism Group of Countable Recursively Saturated Model of PA'

Abstract: I will discuss the question: To what extent does the automorphism group of a countable recursively saturated model of Peano Arithmetic determine the model?

ESC 638

Monday, September 15, 2014

04:45 pm - 06:00 pm

CT Logic Seminar, Philip Scowcroft (Wes): 'Continuous Model Theory for C(X)'

Abstract: In the continuous logic recently developed by Ben Yaacov and others, the class of lattice-ordered groups isomorphic to C(X) with X compact is an elementary class. The theory T of this class has convenient model-theoretic properties: for example, T has a model-completion T(+) which is countably categorical and admits elimination of quantifiers. One may establish also a corresponding Nullstellensatz and determine which models of T have prime-model extensions to models of T(+).

ESC 638

Monday, September 08, 2014

04:45 pm - 06:00 pm

CT Logic Seminar, Reed Solomon (UConn): Reverse mathematics and the Dual Ramsey Theorem

Abstract: This talk will be an introduction to the Dual Ramsey Theorem and to the (relatively few) results in reverse mathematics known about it.

ESC 638

Monday, January 20, 2014

04:45 pm - 06:00 pm

Logic Seminar, Neil Immerman (UMass): 'Descriptive and Dynamic Complexity'

Abstract: An increasing percentage of modern computation is dynamic: a fairly large object is being worked on over a period of time. The object is repeatedly modified and computations are performed. Using auxiliary data structures we can sometimes maintain the ability to very quickly answer certain queries about the object as it changes. dynFO is the set of properties that can be maintained and queried in First-Order logic. Much progress has been made understanding when graph reachability is in dynFO and related classes, but the general question remains open.

ESC 638