economics & mathematics

Topological Opportunities and Breakthrough Innovation in Knowledge Geometry

Institution: the Department of Economics, UMNTC

Duration: May 2026 - Present

Links: [Code] [Paper]

Keywords: Science of Science, Topology, Spectral Graphs Theory, Science Economics, Network Economics, Network Science. 

Abstract

This paper studies whether the geometry, topology, and local spectra of

scientific knowledge networks shape breakthrough innovation. Using the

OGBN-MAG subset of the Microsoft Academic Graph, I construct a dy-

namic scientific knowledge complex from paper-topic assignments, citation

links, authorship, venues, and publication years. The central topological

object is boundary-completion potential: whether a paper’s topic set spans

triangular boundaries already present in the prior topic graph. I also compute

local clique-complex Betti numbers and Laplacian spectral metrics on each

paper’s prior topic-induced graph. Papers published between 2011 and 2016

are linked to their three-year forward citations and classified as breakthrough

papers when they fall in the top five percent of their publication-year citation

distribution. The main evidence shows that boundary-completion potential

and local spectral connectivity are associated with future scientific impact

after controlling for authorship, topic breadth, references, year fixed effects,

and venue-group fixed effects. A causal-style exposure design uses lagged,

leave-venue-out topology shocks from papers in the same fields of study:

external frontier opening strongly shifts a focal paper’s own topological op-

portunity and predicts higher future citations and breakthrough probability.

The results suggest that breakthrough science is not only a function of re-

search scale or centrality, but also of the high-order structure and diffusion

geometry of the knowledge space in which researchers search. 

Outcomes

Y. Lu (2026). The Economic Value of Knowledge Geometry: Topological Opportunities and Breakthrough Innovation in Scientific Research. University of Minnesota. 

A Spatial and Temporal Analysis from 2013 to 2023

Advisor: Prof. Halil Akil(Instructor), Jessie Dickens(Writing Assistant)

Institution: the Department of Economics, UMNTC

Duration: June 2025 - April 2025

Links: [Code] [Paper]

Keywords: Urban/Regional Economics, Economic Development, Convergence Analysis, Spatial Statistics

Abstract

This study investigates the convergence of digital infrastructure across U.S. counties and states from 2013 to 2023, with a focus on whether regional disparities in digital access have narrowed over time. Using microdata from the Integrated Public Use Microdata Series (IPUMS USA), we construct a household-level digital access index based on device and internet connectivity variables. We apply both standard sigma- and beta-convergence models as well as a spatial lag beta-convergence model to evaluate two key hypotheses: (1) initially disadvantaged regions have experienced faster digital growth, and (2) geographically proximate regions converge together through spatial spillovers. Our results provide strong evidence of both sigma- and beta-convergence at the county and state levels, indicating a general reduction in the digital divide. However, we find no robust support for spatial spillovers—regions do not appear to converge faster as a result of their neighbors’ growth. This suggests that while local catch-up dynamics are at play, geographic diffusion of digital development may be limited by policy fragmentation, administrative boundaries, or infrastructure barriers. The findings highlight the need for regional coordination to enhance digital equity.

Outcomes

Y. Lu (2025). Digital Infrastructure Convergence in the United States: Digital Infrastructure Convergence in the United States. University of Minnesota. 

Y. Lu (2025). Digital Infrastructure Convergence in the United States: Digital Infrastructure Convergence in the United States[Computer Software]. Github Repository. https://github.com/HarryLuUMN/Digital-Drifting 

Other

The paper presented at the Undergraduate Economic Workshop, Heller Hurwicz Economic Institute, University of Minnesota, Twin Cities. Apr 2026. 

The paper got the 1st Place at the Undergraduate Economic Writing Competition ($750), University of Minnesota, Twin Cities. Jan 2026. 

This paper got the highest score(1/30) in ECON4331W: Economic Development, Summer 2025, a research writing course in economics major.

Extending Partial Orders: From Binary Relations to Linear Orderings

Advisor: Prof. Karel Prikry

Institution: the School of Mathematics, UMNTC

Duration: September 2025 - December 2025

Links: [Paper]

Keywords: Set Theory, Combinatorics, Ordering Theory

Abstract

In this paper, we will explore the relationship between the two kinds of orderings, namely partial orderings and linear orderings. 

The two key theorems that we will discuss are the Hausdorff maximality theorem, that every partial ordering contains a maximal linearly ordered subset, and the linear extension theorem, discussed first by Polish mathematicians in 1920's, that every partial ordering can be extended to a linear ordering. Our main source is Linear Operators Part 1 by N. Dunford and J. T. Schwartz, which we will refer to as LO. 

Outcomes

Y. Lu (2025). Extending Partial Orders: From Binary Relations to Linear Orderings. University of Minnesota.