**Contact Information:**

**Name:** Vince Guingona

**Office:** YR 357

**Office Hours:** Monday / Wednesday 2 - 3:30pm or by appointment

**Email:** vguingona (at) towson (dot) edu

**Introduction:**

Greetings! My name is Vince Guingona and I am an Assistant Professor in Mathematics at Towson University. 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 VC-minimal theories, VC-density, NIP theories, and definability of types. I am also interested in applications of model theory to algebra, combinatorics, and computational learning theory. I did my undergraduate work at the University of Chicago, and I am originally from Western Massachusetts.

**Employment History:**

- Assistant Professor - Towson University (August 2016 to Present)
- Visiting Assistant Professor - Wesleyan University (September 2015 to June 2016)
- Postdoctoral Research Fellow - Ben-Gurion University of the Negev (August 2014 to June 2015)
- 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)

"On definability of types in dependent theories" (Defense Slides, Abstract, Thesis)*Thesis:*

Dr. M. Chris Laskowski*Advisor:*

**Undergraduate:**University of Chicago. (graduated: June 2005)**High School:**Mohawk Trail Regional High School, Buckland, MA. (graduated: June 2001)

**Papers:**

- On positive local combinatorial dividing-lines in model theory, Joint with: Cameron Donnay Hill -
*Archive for Mathematical Logic*, Accepted.**Abstract:**We introduce the notion of positive local combinatorial dividing-lines in model theory. We show these are equivalently characterized by indecomposable algebraically trivial Fraisse classes and by complete prime filter classes. We exhibit the relationship between this and collapse-ofindiscernibles dividing-lines. We examine several test cases, including those arising from various classes of hypergraphs.

(arXiv 1702.06102, Archive for Mathematical Logic)

- Characterizing model-theoretic dividing lines via collapse of generalized indiscernibles, Joint with: Cameron Donnay Hill and Lynn Scow -
*Annals of Pure and Applied Logic*.**Abstract:**We use the notion of collapse of generalized indiscernible sequences to classify various model-theoretic dividing lines. In particular use the collapse of*n*-multi-order indiscernibles to characterize op-dimension*n*; collapse of function-space indiscernibles (i.e., parameterized equivalence relations) to characterize rosy theories; and finally, convex equivalence relation indiscernibles to characterize NTP2 theories.

(Modnet Preprint 963, arXiv 1511.07245, Annals of Pure and Applied Logic)

- On VC-density in VC-minimal theories, submitted.
**Abstract:**We show that any formula with two free variables in a VC-minimal theory has VC-codensity at most two. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acl^{eq}= dcl^{eq}, the VC-codensity of a formula is at most the number of free variables.

(Modnet Preprint 778, arXiv 1409.8060)

- A Local Characterization of VC-Minimality, Joint with: Uri Andrews -
*Proceedings of the American Mathematical Society*,**144**(2016), 2241-2256.**Abstract:**We show VC-minimality is Π^{0}_{4}-complete. In particular, we give a local characterization of VC-minimality. We also show dp-smallness is Π^{1}_{1}-complete.

(Proceedings of the AMS)

- On a Common Generalization of Shelah's 2-Rank, dp-Rank, and o-Minimal Dimension, Joint with: Cameron Donnay Hill -
*Annals of Pure and Applied Logic*,**166**(2015), 502-525.**Abstract:**In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multiorder property, generalizing the order property, and use this to create op-rank, which generalizes 2-rank. From this we build op-dimension. We show that op-dimension bounds dp-rank, that op-dimension is sub-additive, and op-dimension generalizes o-minimal dimension in o-minimal theories.

(Modnet Preprint 605, arXiv 1307.4113, Annals of Pure and Applied Logic)

- On VC-Density Over Indiscernible Sequences, Joint with: Cameron Donnay Hill -
*Mathematical Logic Quarterly*,**60**(2014), 59-65.**Abstract:**In this paper, we study VC-density over indiscernible sequences (denoted VC_{ind}-density). We answer an open question in [1], showing that VC_{ind}-density is always integer valued. We also show that VC_{ind}-density and dp-rank coincide in the natural way.

(Modnet Preprint 363, arXiv 1108.2554, Mathematical Logic Quarterly)

- On VC-Minimal Fields and dp-Smallness,
*Archive for Mathematical Logic*,**53**(2014), 503-517.**Abstract:**In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.

(Modnet Preprint 609, arXiv 1307.8004, Archive for Mathematical Logic)

- Convexly Orderable Groups and Valued Fields, Joint with: Joseph Flenner -
*Journal of Symbolic Logic*,**79**(2014), 154-170.**Abstract:**We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also considered, including a necessary condition for a theory of valued fields to be quasi-VC-minimal. For example, the*p*-adics are not quasi-VC-minimal.

(Modnet Preprint 505, arXiv 1210.0404, JSL on Cambridge Journals)

- Canonical Forest in Directed Families, Joint with: Joseph Flenner -
*Proceedings of the American Mathematical Society*,**142**(2014), 1849-1860.**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, Proceedings of the AMS)

- On VC-Minimal Theories and Variants, Joint with: Michael C. Laskowski -
*Archive for Mathematical Logic*,**52**, (2013), 743-758.**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, Archive for Mathematical Logic)

- On Uniform Definability of Types over Finite Sets -
*Journal of Symbolic Logic*,**77**(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:**

*Generalized Indiscernbiles and Dividing Lines*(AMS Special Session, Hunter College CUNY -- May 6, 2017)*Fraisse Classes and Model-Theoretic Dividing Lines*(Midwest Model Theory Day -- April 4, 2017)*Generalized Indiscernibles and Dividing Lines*(AMS Sectional Meeting, Indiana University -- April 2, 2017)*On Collapse of Generalized Indiscernibles*(CUNY Model Theory Seminar -- October 28, 2016)*VC-Density: what we know and what we don't know*(Northeast Regional Model Theory Days -- October 22, 2016)*Computing VC-Density*(Model Theory Special Session - The 2016 North American Annual Meeting of the ASL -- May 26, 2016)*On Generalized Notions of Dimension*(Wesleyan Math/CS Colloquium -- November 19, 2015)*On VC-density in VC-minimal theories*(CUNY Logic Workshop -- October 23, 2015)*VC-Minimality, Convex Orderability, and dp-Smallness*(Southern Wisconsin Logic Colloquium -- September 29, 2015)*A Local Characterization of VC-Minimality*(Connecticut Logic Seminar -- September 21, 2015)*VC-density in VC-minimal theories*(CMO Neostability Theory Conference -- July 14, 2015)*On VC-minimal theories*(UC Berkeley Model Theory Seminar -- March 26, 2014)*VC-density, dp-rank, and op-dimension*(Carnegie Mellon Model Theory Seminar -- November 11, 2013)*On classifying VC-minimal theories*(Hebrew University Logic Seminar -- March 13, 2013)*VC-density over indiscernible sequences*(Very Informal Gathering of Logicians at UCLA -- February 1, 2013)*On convexly orderable groups and valued fields*(CUNY Logic Workshop -- October 26, 2012)*VC-Density over indiscernible sequences*(Ohio State Logic Seminar -- April 10, 2012)*On VC-minimality in Algebraic Structures*(Model Theory Special Session - The 2012 North American Annual Meeting of the ASL -- April 3, 2012)*On VC-minimal theories*(Special Session on Model Theory - 2012 Spring Western Section Meeting -- March 3, 2012)*Recent developments on VC-minimal theories*(UW Madison Logic Seminar -- February 14, 2012)*On uniform definability of types over finite sets*(Model Theory Special Session - The 2011 North American Annual Meeting of the ASL -- March 26, 2011)*Definability of types and compression schemes*(University of Illinois at Chicago Logic Seminar -- February 1, 2011)*Definability of types and VC-density*McMaster University Model Theory Seminar -- January 18, 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 -- January 7, 2011)*Compression Schemes and Definability of Types*(George Washington University Logic Seminar -- October 6 and 13, 2010)*Dependence and Definability of Types*(Notre Dame Logic Seminar -- April 15, 2010)*Learning Theory and Model Theory*(George Washington University Math Graduate Student Seminar -- February 20, 2009)

**Other Research:**

- I was a referee for the Notre Dame Journal of Formal Logic from Fall 2011 to Fall 2013.
- I participated in the Model Theory, Arithmetic Geometry and Number Theory at the Mathematical Sciences Research Institute, Berkeley, California, Spring 2014.
- I was the organizer for the Notre Dame Logic Seminar for Fall 2013.
- I participated in the Model Theory 2013 conference in Ravello, Italy, June 10 through June 15, 2013.
- I participated in the Workshop on Model Theory: Groups, Geometry, and Combinatorics in Olberwolfach, Germany, January 6 through January 12, 2013 (and they have this picture of me).
- I participated in the Neostability Theory workshop at the Banff International Research Station, January 29 through February 3, 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, June 19 through June 26, in Snowbird Resort, Utah.
- I participated in the University of Chicago Summer REU Program, Summer 2003 and Summer 2004.

**Teaching:**

- MATH 273-001,
*Calculus I*, Spring 2019 -- Monday 8 - 9:50pm YR 103 / Wednesday 8 - 9:50pm YR 126 / Friday 8 - 8:50am YR 126 - MATH 267-001,
*Introduction to Abstract Mathematics*, Spring 2019 -- Monday/Wednesday 12 - 1:50pm - YR 128 - MATH 273-001,
*Calculus I*, Fall 2018 -- Monday 9 - 10:50pm YR 103 / Wednesday 9 - 10:50pm YR 126 / Friday 10 - 10:50am YR 126 - MATH 369-001,
*Introduction to Abstract Algebra*, Fall 2018 -- Monday/Wednesday 8 - 8:50am, Friday 8 - 9:50am - YR 127 - MATH 274-002,
*Calculus II*, Spring 2018 -- Monday 11 - 12:50pm YR 126 / Wednesday 11 - 12:50pm YR 103 / Friday 11 - 11:50am YR 126 - MATH 267-001,
*Introduction to Abstract Mathematics*, Spring 2018 -- Monday/Wednesday 9 - 9:50am, Friday 8 - 9:50am - YR 127 - MATH 274-101,
*Calculus II*, Fall 2017 -- Monday 4:30 - 6:45pm - YR 126 / Wednesday 4:30 - 5:20pm - YR 103 / Wednesday 5:30 - 6:45pm - YR 129 - MATH 369-001,
*Introduction to Abstract Algebra*, Fall 2017 -- Monday/Wednesday 12 - 12:50pm, Friday 12 - 1:50pm - YR 122 - MATH 274-004,
*Calculus II*, Spring 2017 -- Monday/Wednesday from 10:00am to 11:50am - YR 129 (Lab: Monday from 11:00am to 11:50am - YR 103) - MATH 267-001,
*Introduction to Abstract Mathematics*, Spring 2017 -- Monday 8 - 9:50pm, Wednesday/Friday 9 - 9:50am - YR 123 - MATH 274-001,
*Calculus II*, Fall 2016 -- Tuesday/Thursday from 8:00am to 9:15am - YR 126 (Lab: Monday from 8:00am to 9:50am - YR 103) - MATH 473-180,
*Introductory Real Analysis*, Fall 2016 -- Monday/Wednesday from 1:00pm to 2:50pm - YR 127 - MATH223-02,
*Linear Algebra*, Spring 2016 -- Monday/Wednesday/Friday from 9:00am to 9:50am - Exley 137 - MATH262-01,
*Abstract Algebra*, Spring 2016 -- Monday/Wednesday/Friday from 10:00am to 10:50am - Exley 137 - Graduate Reading Course on
*p*-adics and Valued Fields, Spring 2016 -- Exley 618 - MATH121-03,
*Calculus I, Part I*, Fall 2015 -- Tuesday/Thursday from 1:10pm to 2:30pm - Exley 121 - MATH221-01,
*Vectors and Matrices*, Fall 2015 -- Tuesday/Thursday from 10:30am to 11:50am - Exley 121 - I gave a three-part lecture series titled "Model Theory and Computational Learning Theory" at Ben-Gurion, Fall 2014.
- I was the lecturer for Beginning Logic, MATH 10130, at Notre Dame, Fall 2013.
- I was the lecturer for Topics in Mathematical Logic, "NIP Theories and Computational Learning Theory," MATH 80510, at Notre Dame, Fall 2013.
- I was the lecturer for Calculus III, MATH 20550, at Notre Dame, Spring 2013.
- I was the lecturer for Calculus III, MATH 20550, at Notre Dame, Fall 2012.
- I was the lecturer for Calculus B, MATH 10360, at Notre Dame, Spring 2012.
- I was the lecturer for Calculus A, MATH 10350, at Notre Dame, Fall 2011.
- I substituted for MATH 713 at Maryland, three weeks of Spring 2011.
- I was a TA for MATH 220 at Maryland, Fall 2006 and Fall 2009.
- I was a TA for MATH 141 at Maryland, Spring 2007.
- I was an advisor for the undergraduate math club at Maryland, Fall 2007.
- I was a grader for MATH 405 at Maryland, Spring 2008.

**Last updated:** September 11, 2018.