Vincent Guingona's Mathematics Webpage

Contact Information:

Name: Vincent Guingona
Office: 118 Hayes–Healy
Office Hours: Monday and Wednesday, 4pm to 6pm (or by appointment)
Email: guingona (dot) 1 (at) nd (dot) edu

Introduction:

Greetings! My name is Vincent Guingona and I am currently a postdoc at the University of Notre Dame. I received my Ph.D. in mathematics from the University of Maryland College Park under the direction of Chris Laskowski. My research interests include Model Theory, specifically Dependent Theories and Definability of Types. I did my undergraduate work at the University of Chicago, and I am originally from Western Massachusetts.

My CV, My Publication List, My Graduate Thesis.

Employment History:

• Visiting Assistant Professor - University of Notre Dame, Department of Mathematics. (July 2011 to June 2014)

Education:

• Graduate School: University of Maryland, Department of Mathematics. (graduated: May 2011)
    Thesis: "On definability of types in dependent theories" (Defense Slides, Abstract, Thesis)
    Advisor: Dr. M. Chris Laskowski
  
• Undergraduate: University of Chicago. (graduated: June 2005)
• High School: Mohawk Trail Regional High School, Buckland, MA. (graduated: June 2001)

Papers:

• Convex Orderability in Groups and Valued Fields, Joint with: Joseph Flenner (in preparation)
• Canonical Forest in Directed Families, Joint with: Joseph Flenner (submitted 10 November 2011)
  Abstract: Two uniqueness results on representations of sets constructible in a directed family of sets are given. In the unpackable case, swiss cheese decompositions are unique. In the packable case, they are not unique but admit a quasi-ordering under which the minimal decomposition is unique. Both cases lead to a one-dimensional elimination of imaginaries in VC-minimal and quasi-VC-minimal theories.
  (Modnet Preprint 379, arXiv 1111.2843)
• On VC-Minimal Theories and Variants, Joint with: Michael C. Laskowski (submitted 18 October 2011)
  Abstract: In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablility and show that this lies strictly between VC-minimality and dp-minimality. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion full VC-minimality, show that this lies strictly between weak o-minimality and VC-minimality, and show that theories that are fully VC-minimal have low VC-density.
  (Modnet Preprint 364, arXiv 1110.4274)
• Local dp-Rank and VC-Density over Indiscernible Sequences, Joint with: Cameron Donnay Hill (submitted 11 August 2011)
  Abstract: In this paper, we study a localized version of dp-rank and show this local version relates to the standard global dp-rank in the natural way. We also show that local dp-rank, VC-density over indiscernible sequences (VC_ind-density), and UDTFS-rank over indiscernible sequences are all identical. As a corollary, in any dp-minimal theory, the VC_ind-density of a formula is bounded by the length of its free variables.
  (Modnet Preprint 363, arXiv 1108.2554)
• Definability of Types over Finite Partial Order Indiscernibles (submitted 10 August 2011)
  Abstract: In this paper, we show that a partitioned formula φ is dependent if and only if φ has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by giving a decomposition of the truth values of an externally definable formula on a finite partial order indiscernible.
  (Modnet Preprint 347, arXiv 1108.2499)
• On Uniform Definability of Types over Finite Sets - Journal of Symbolic Logic, Volume 77, Issue 2 (2012), 499-514.
  Abstract: In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.
  (Modnet Preprint 250, arXiv 1005.4924, JSL on Project Euclid)
• Dependence and Isolated Extensions - Proceedings of the American Mathematical Society, 139 (2011), 3349-3357
  Abstract: In this paper, we show that φ is a dependent formula if and only if all φ-types have an extension to a φ-isolated φ-type that is an "elementary φ-extension" (see Definition 2.3 in the paper). Moreover, we show that the domain of this extension adds at most 2 times the independence dimension of φ new elements to the domain of the original φ-type. We give corollaries to this theorem and discuss parallels to the stable setting.
  (Modnet Preprint 212, arXiv 0911.1361, Proceedings of the AMS)

Invited Talks:

• VC-Density over Indiscernible Sequences (Ohio State Logic Seminar -- 10 April 2012
• On VC-minimality in Algebraic Structures (Model Theory Special Session - The 2012 North American Annual Meeting of the ASL -- 3 April 2011)
• On VC-minimal theories (Special Session on Model Theory - 2012 Spring Western Section Meeting -- 3 March 2012)
• Recent developments on VC-minimal theories (UW Madison Logic Seminar -- 14 February 2012)
• On uniform definability of types over finite sets (Model Theory Special Session - The 2011 North American Annual Meeting of the ASL -- 26 March 2011)
• Definability of types and compression schemes (University of Illinois at Chicago Logic Seminar -- 1 February 2011)
• Definability of types and VC-density (McMaster University Model Theory Seminar -- 18 January 2011)
• On definability of types in dependent theories (AMS Special Session, Model Theory of Fields and Applications - The 2011 Joint Mathematics Meeting in New Orleans -- 7 January 2011)
• Compression Schemes and Definability of Types (George Washington University Logic Seminar -- 6 and 13 October 2010)
• Dependence and Definability of Types (Notre Dame Logic Seminar -- April 15th, 2010)
• Learning Theory and Model Theory (George Washington University Math Graduate Student Seminar -- 20 February 2009)

Other Research:

• I am a referee for the Notre Dame Journal of Formal Logic.
• I participated in the Neostability Theory workshop at the Banff International Research Station, 29 January through 3 February 2012.
• I was the organizer for the Maryland Logic Seminar for Fall 2010 and Spring 2011.
• I participated in the Mathematics Research Community 2010 -- Model Theory of Fields, 19 June through 26 June in Snowbird Resort, Utah.
• I participated in the University of Chicago Summer REU Program, Summer 2003 and Summer 2004.

Teaching:

Current Class: Calculus B (Math 10360, Section 6, MWF 12:50pm to 1:40pm, 129 Hayes-Healy)
Previous Classes:
• I was the lecturer for Calculus A, MATH 10350, at Notre Dame, Fall 2011.
• I substituted for MATH 713, three weeks of Spring 2011.
• I was a TA for MATH 220, Fall 2006 and Fall 2009.
• I was a TA for MATH 141, Spring 2007.
• I was an advisor for the undergraduate math club, Fall 2007.
• I was a grader for MATH 405, Spring 2008.

External Links:

Other Websites:
• University of Notre Dame Department of Mathematics Website
• Modnet Preprints
• arXiv
• Proceedings of the American Mathematical Society
• Chris Laskowski's Webpage

Fun Stuff:

• Pictures
• My web comic

Last updated: 11 April 2012.