It will be held in Carlo Auditorium, Tegeler Hall on Friday, May 2nd, from 4pm to 6pm. 

The Case Lecture is the highlight of the Annual Awards Ceremony for the Department of Mathematics and Statistics.  Students at all levels of study will be recognized for their outstanding achievements in mathematics and statistics.  Family and friends are welcome.

This year Case Lecture will be given by Dr. John McCarthy, Spencer T. Olin Professor of Mathematics from Washington University in St. Louis.

Title: Mathematics as Liberal Art

Title:  Mathematics Education in Community Colleges: An Overview & Conversation

Abstract:  Teaching mathematics in community colleges shares a lot in common with teaching in university settings, but also confronts special challenges and opportunities. This presentation will offer an opportunity to learn about and discuss how St. Louis Community College contributes to the mathematics education community in St. Louis, the region, and nationally.

Title:  How to choose your own mathematical adventures

Abstract:  What is mathematical research? How does a mathematician find problems to work on? How does one build mathematical collaborations? In this talk, I will share my journey to research mathematics, what it entails, how I have developed new research ideas, and how I have found my place within the mathematical community. Mathematical topics of discussion will include lattice point visibility, parking functions, and a connection between vector partition functions and juggling. No prior mathematical background on these topics is expected nor assumed as we will introduce all of the needed concepts from first principles. All that is needed is the willingness to wonder and ask the question: “what happens if…?”

Title:  Standards Based Grading at Harris-Stowe State University (HSSU) : Our Journey so Far

Abstract:  Accurately evaluating student learning and connecting that to student grades is important for all instructors, not only for course and self-evaluation, but for accurate data collection for program and course success. Traditional grading methods sometimes hide the concrete learning objectives that students master throughout a course for favor of a single number that overall represents the student’s success (and hopefully learning) in a course. With this, we decided to explore implementing Standards Based Grading (in some form) at HSSU for selected math courses in the 2024-2025 academic year. We will discuss the rationale of switching to this grading style in some courses (and why not others), specific details of how we implemented these concepts in our courses, the pros and cons comparing them to traditional grading methods, and most importantly, the lessons we learned and our ongoing process of improving this for the future. In addition, this change has led to productive discussions across the university among colleagues, administrators, and students on best practices for student understanding and engagement in the classroom.

Title:  Survey of Calculus

Abstract:  TBA

Title: Some research I did as an undergraduate, and what has happened since

Abstract:  I will discuss an REU project that I worked on in Summer 2012 concerning certain projections of knots called “petal diagrams.” The main thing I will prove is that that every knot has a petal diagram. This 2012 result led to the introduction, by other researchers, of a model for random knots called the Petaluma model. I will discuss the theorem that a random knot in the Petaluma model is nontrivial with high probability. I also hope to touch on what it was like to do this research as an undergraduate, and how it influenced me.

Title: Creating and Maintaining Effective Undergraduate Peer Mathematics Tutoring: A Conversation

Abstract:  Creating an effective and inclusive undergraduate mathematics tutoring program requires a careful approach at every stage, from tutor selection to faculty and institutional support. This talk will outline an approach to structuring a tutoring program that fosters both accessibility and academic success. First, we emphasize the importance of selecting tutors based not only on mathematical proficiency but also on character qualities such as patience, empathy, and integrity. Next, we discuss the need for rigorous, evidence-based training that prepares tutors to support diverse learners effectively, including those who have historically struggled in mathematics. Additionally, targeted outreach is crucial to ensuring students in lower-level math courses—who often stand to benefit the most—utilize tutoring services. Finally, sustainable success requires collaboration between faculty and institutional support services, ensuring a shared commitment to student achievement. By implementing these strategies, mathematics tutoring programs can become inclusive and effective, as evidenced by the early success of the Math Success Center at Lindenwood University. We will also have a dialogue about some of the challenges that can arise in undergraduate tutoring, including the potential for academic integrity violations, misinformation from ill-equipped tutors, and fears of encouraging learned helplessness in tutees.

Title: The mother of all 3-manifolds

Abstract: I will discuss a proof of the famous result of Lickorish and Wallace that every closed, orientable, connected 3-manifold can be obtained by performing Dehn surgery on a link in the 3-sphere.

Title: Asymptotically geodesic surfaces in hyperbolic 3-manifolds

Abstract: Let M be a hyperbolic 3-manifold. We say a sequence of distinct (non-commensurable) essential closed surfaces in M is asymptotically geodesic if their principal curvatures go uniformly to zero. When M is closed, these sequences exist abundantly by the Kahn-Markovic surface subgroup theorem, and we will discuss the fact that such surfaces are always asymptotically dense, even though they might not equidistribute. We will also talk about the fact that such sequences do not exist when M is geometrically finite of infinite volume. Finally, time permitting, we will discuss some partial answers to the question: does the existence of asymptotically geodesic surfaces in a negatively-curved 3-manifold imply the manifold is hyperbolic? This is joint work with Ben Lowe.

Title: An Introduction To Symplectic Manifolds

Abstract: Symplectic manifolds have been an object of study in mathematical physics from classical mechanics to string theory. In this talk we will introduce the symplectic form, Hamiltonians, and Lagrangian submanifolds with examples. We will end with connections to modern research. This talk is suitable for anyone with an understanding of manifolds and differential forms.

Title: From Lorentzian manifolds to signature-type change

Abstract: Hartle and Hawking (1983) suggested that signature-type change could have profound conceptual implications, leading to the development of the "no-boundary" proposal for the universe’s initial conditions. In this frame- work, singularity-free universes have no distinct beginning yet possess an origin of time. Mathematically, this corresponds to manifolds with a smooth transition from a Riemannian to a Lorentzian signature, where time emerges at the interface. Motivated by the "no-boundary" proposal, I explore this topic and introduce elements of a novel framework for signa- ture changing manifolds, characterized by a smooth yet degenerate met- ric. Additionally, I extend certain Lorentzian techniques and results to the context of signature change.

Title: New Minimal Lagrangians in ℂℙ2

Abstract: Minimal Lagrangian tori in ℂℙ2 are the expected local model for particular point singularities of Calabi-Yau 3-folds, and numerous examples have been constructed. In stark contrast, very little is known about higher genus examples, with the only ones to date due to Haskins-Kapouleas and only in odd genus. Using loop group methods, we construct new examples of minimal Lagrangian surfaces of genus (k-1)(k-2)/2 for large k. In particular, we construct the first examples of such surfaces with even genus. This is joint work with Sebastian Heller and Franz Pedit.