**Contact Information:**

**Name:** Vince Guingona

**Office:** YR 226

**Office Hours:** Monday / Wednesday 2pm to 3:30pm, Friday 11am to 11:50am, or by appointment

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

**Introduction:**

Greetings! My name is Vince Guingona and I am an Associate 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 machine learning. I did my undergraduate work at the University of Chicago, and I am originally from Western Massachusetts.

**Employment History:**

- Associate Professor - Towson University (August 2023 to Present)
- Assistant Professor - Towson University (August 2016 to August 2023)
- 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:**

- Indivisibility for classes of graphs, Joint with: Felix Nusbaum, Zain Padamsee, Miriam Parnes, Christian Pippin, and Ava Zinman, submitted.
**Abstract:**We examine indivisibility for classes of graphs. We show that the class of hereditarily α-sparse graphs is indivisible if and only if α > 2. Additionally, we show that the following classes of graphs are indivisible: perfect graphs, cographs, and chordal graphs, and the following classes of graphs are not indivisible: threshold graphs, split graphs, and distance-hereditary graphs.

(arXiv 2312.01466)

- Littlestone and VC-dimension of families of zero sets, Joint with: Alexei Kolesnikov, Julie Nierwinski, and Richard Soucy, submitted.
**Abstract:**We prove that, for any*d*linearly independent functions from some set into a*d*-dimensional vector space over any field, the family of zero sets of all non-trivial linear combination of these functions has VC-dimension and Littlestone dimension*d*- 1. Additionally, we characterize when such families are maximal of VC-dimension*d*- 1 and give a sufficient condition for when they are maximal of Littlestone dimension*d*- 1.

(arXiv 2109.04805)

- Products of classes of finite structures, Joint with: Miriam Parnes and Lynn Scow,
*Notre Dame Journal of Formal Logic*, to appear.**Abstract:**We study the preservation of certain properties under products of classes of finite structures. In particular, we examine age indivisibility, indivisibility, definable self-similarity, the amalgamation property, and the disjoint*n*-amalgamation property. We explore how each of these properties interact with the wreath product, direct product, and free superposition of classes of structures. Additionally, we consider the classes of theories which admit configurations indexed by these products.

(arXiv 2111.08120)

- The Brezis-Nirenberg problem for systems involving divergence-form operators, Joint with: Burton Brown IV, Mathew Gluck, Thomas Hammons, Miriam Parnes, Sean Pooley, and Avery Schweitzer,
*Nonlinear Differential Equations and Applications*,**30**75 (2023).**Abstract:**We study a system of nonlinear elliptic partial differential equations involving divergence-form operators. The problem under consideration is a natural generalization of the classical Brezisâ€“Nirenberg problem. We find conditions on the domain, the coupling coefficients and the coefficients of the differential operator under which positive solutions are guaranteed to exist and conditions on these objects under which no positive solution exists.

- Comparing approximate and probabilistic differential privacy parameters, Joint with: Alexei Kolesnikov, Julie Nierwinski, and Avery Schweitzer,
*Information Processing Letters*,**182**, (2023).**Abstract:**This paper compares two notions of differential privacy: approximate differential privacy (ADP) and probabilistic differential privacy (PrDP). It is well-known that the PrDP implies the ADP; and it was established in [7] that the ADP implies the PrDP, after a penalty on the parameters ε and δ that are used in the deffnitions of both properties. We investigate how large do these penalties have to be. We show, in particular, that if the penalty on δ is O(δ), then the penalty on ε has to be bounded away from zero.

(Information Processing Letters)

- Ranks based on strong amalgamation Fraisse classes, Joint with: Miriam Parnes,
*Archive for Mathematical Logic*, (2023), 1-41.**Abstract:**In this paper, we introduce the notion of**K**-rank, where**K**is an algebraically trivial Fraisse class. Roughly speaking, the**K**-rank of a partial type is the number of independent "copies" of**K**that can be "coded" inside of the type. We study**K**-rank for specific examples of**K**, including linear orders, equivalence relations, and graphs. We discuss the relationship of**K**-rank to other well-studied ranks in model theory, including dp-rank and op-dimension.

(arXiv 2007.02922, Archive for Mathematical Logic)

- On VC-density in VC-minimal theories -
*Notre Dame Journal of Formal Logic*,**63**(3), (2022), 395-413.**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)

- On positive local combinatorial dividing-lines in model theory, Joint with: Cameron Donnay Hill -
*Archive for Mathematical Logic*,**58**, (2019), 289â€“323.**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*,**168**, (2017), 1091-1111.**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)

- 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:**

*Model theory and differential privacy*(The 2022 North American Annual Meeting of the ASL -- April 9, 2022)*Computing VC-density*(Logic Seminar, George Washington University -- November 22, 2019)*Ranks in NIP Theories*(Model Theory and Mathematical Logic, University of Maryland, College Park -- June 23, 2019)*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 an organizer for the Model Theory and Mathematical Logic conference at the University of Maryland, College Park in June 2019.
- 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 a referee for peer-reviewed publications from Fall 2011 to present.
- 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 273-002,
*Calculus I*, Spring 2024 -- Monday/Wednesday 10 - 11:50am / Friday 10 - 10:50am - MATH 490-001,
*Senior Seminar*, Sprint 2024 -- Monday/Wednesday/Friday 9 - 9:50am- Topics will include: VC-dimension, Littlestone-dimension, PAC-learning, Online learning, Recursive teaching, etc.

- MATH 273-003,
*Calculus I*, Fall 2023 -- Monday/Wednesday 12 - 1:50pm / Friday 12 - 12:50pm - MATH 315-001,
*Applied Combinatorics*, Fall 2023 -- Monday/Wednesday 9 - 10:50am - MATH 273-001,
*Calculus I*, Spring 2023 -- Monday/Wednesday 8 - 9:50am / Friday 8 - 8:50am - MATH 267-001,
*Introduction to Abstract Mathematics*, Spring 2023 -- Monday/Wednesday 2 - 3:50am - MATH 273-001,
*Calculus I*, Fall 2022 -- Monday/Wednesday 8 - 9:50am / Friday 8 - 8:50am - MATH 451-001,
*Graph Theory*, Fall 2022 -- Monday/Wednesday/Friday 10 - 10:50am - MATH 273-003,
*Calculus I*, Spring 2022 -- Monday/Wednesday 8 - 9:50am YR 129 / Friday 9 - 9:50am YR 217 - MATH 267-001,
*Introduction to Abstract Mathematics*, Spring 2022 -- Wednesday 10 - 11:50am YR 219 / Friday 10 - 11:50am YR 129 - MATH 273-001,
*Calculus I*, Fall 2021 -- Monday/Wednesday 8 - 9:50am / Friday 8 - 8:50am YR 218 - MATH 265-002,
*Elementary Linear Algebra*, Fall 2021 -- Wednesday/Friday 10 - 11:50am YR 219 - MATH 273-002,
*Calculus I*, Spring 2021 -- Monday/Wednesday 8 - 9:50am / Friday 8 - 8:50am Online - MATH 273-003,
*Calculus I*, Spring 2021 -- Monday/Wednesday 10 - 11:50am / Friday 11 - 11:50am Online - MATH 273-004,
*Calculus I*, Fall 2020 -- Monday 12 - 1:50pm YR 130 / Wednesday 12 - 1:50pm YR 217 / Friday 12 - 12:50am Online - MATH 477-001,
*Topology*, Fall 2020 -- Monday/Wednesday/Friday 9 - 9:50am Online - MATH 273-005,
*Calculus I*, Spring 2020 -- Monday/Wednesday 12 - 1:50pm YR 217 / Friday 12 - 12:50pm YR 217 - MATH 267-001,
*Introduction to Abstract Mathematics*, Spring 2020 -- Monday/Wednesday 8 - 9:50am - YR 128 - MATH 273-001,
*Calculus I*, Fall 2019 -- 8 - 9:50am YR 217 / Wednesday 8 - 9:50am YR 219 / Friday 9 - 9:50am YR 219 - MATH 315-001,
*Applied Combinatorics*, Fall 2019 -- Monday/Wednesday 12 - 1:50pm YR 216 - MATH 273-001,
*Calculus I*, Spring 2019 -- Monday 8 - 9:50am YR 103 / Wednesday 8 - 9:50am 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 - 10:50am YR 103 / Wednesday 9 - 10:50am 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 the University of Maryland College Park, three weeks of Spring 2011.
- I was a TA for MATH 220 at the University of Maryland College Park, Fall 2006 and Fall 2009.
- I was a TA for MATH 141 at the University of Maryland College Park, Spring 2007.
- I was an advisor for the undergraduate math club at the University of Maryland College Park, Fall 2007.
- I was a grader for MATH 405 at the University of Maryland College Park, Spring 2008.

**Last updated:** December 5, 2023.