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1. Cohomology on the incidence correspondence and related questions

Author

Kyomuhangi, Annet, Marangone, Emanuela, Raicu, Claudiu, and Reed, Ethan

Subjects
Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, Mathematics - Representation Theory, 14M15, 14C20, 20G05, 20G15, 05E05, 13A35
Abstract

We study a variety of questions centered around the computation of cohomology of line bundles on the incidence correspondence (the partial flag variety parametrizing pairs consisting of a point in projective space and a hyperplane containing it). Over a field of characteristic zero, this problem is resolved by the Borel-Weil-Bott theorem. In positive characteristic, we give recursive formulas for cohomology, generalizing work of Donkin and Liu in the case of the 3-dimensional flag variety. In characteristic 2, we provide non-recursive formulas describing the cohomology characters in terms of truncated Schur polynomials and Nim symmetric polynomials. The main technical ingredient in our work is the recursive description of the splitting type of vector bundles of principal parts on the projective line. We also discuss properties of the structure constants in the graded Han-Monsky representation ring, and explain how our cohomology calculation characterizes the Weak Lefschetz Property for Artinian monomial complete intersections.

Published
2024

2. An Isomorphism Theorem for Arithmetic Complexes

Author

Fiorindo, Luca, Reed, Ethan, Roshan-Zamir, Shahriyar, and Yu, Hongmiao

Subjects
Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, Mathematics - Combinatorics, 13D02, 14F06, 05A19, 20G10
Abstract

We consider generalizations of certain arithmetic complexes appearing in work of Raicu and VandeBogert in connection with the study of stable sheaf cohomology on flag varieties. Defined over the ring of integer valued polynomials, we prove an isomorphism of these complexes as conjectured by Gao, Raicu, and VandeBogert. In particular, this gives a more conceptual proof of an identification between the stable sheaf cohomology of hook and two column partition Schur functors applied to the cotangent sheaf of projective space.

Published
2023

3. Nisin Inhibition of Gram-Negative Bacteria.

Author

Charest, Adam M., Reed, Ethan, Bozorgzadeh, Samantha, Hernandez, Lorenzo, Getsey, Natalie V., Smith, Liam, Galperina, Anastasia, Beauregard, Hadley E., Charest, Hailey A., Mitchell, Mathew, and Riley, Margaret A.

Subjects
GRAM-negative bacteria, NISIN, LACTOCOCCUS, INFECTION control, PHYTOPATHOGENIC bacteria, HELICOBACTER, ACINETOBACTER
Abstract

Aims: This study investigates the activity of the broad-spectrum bacteriocin nisin against a large panel of Gram-negative bacterial isolates, including relevant plant, animal, and human pathogens. The aim is to generate supportive evidence towards the use/inclusion of bacteriocin-based therapeutics and open avenues for their continued development. Methods and Results: Nisin inhibitory activity was screened against a panel of 575 strains of Gram-negative bacteria, encompassing 17 genera. Nisin inhibition was observed in 309 out of 575 strains, challenging the prevailing belief that nisin lacks effectiveness against Gram-negative bacteria. The genera Acinetobacter, Helicobacter, Erwinia, and Xanthomonas exhibited particularly high nisin sensitivity. Conclusions: The findings of this study highlight the promising potential of nisin as a therapeutic agent for several key Gram-negative plant, animal, and human pathogens. These results challenge the prevailing notion that nisin is less effective or ineffective against Gram-negative pathogens when compared to Gram-positive pathogens and support future pursuits of nisin as a complementary therapy to existing antibiotics. Significance and Impact of Study: This research supports further exploration of nisin as a promising therapeutic agent for numerous human, animal, and plant health applications, offering a complementary tool for infection control in the face of multidrug-resistant bacteria. [ABSTRACT FROM AUTHOR]

Published
2024
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6. Not simply for entertainment : the failure of Kahani hamare Mahabharat ki and its place in a new generation of televised Indian mythology

Author

Burnam, Reed Ethan

Subjects
Kahani hamare Mahabharat ki, Televised Mahabharat, Indian televised mythology, Television mythology
Abstract

This thesis looks at the media event of Kahani Hamare Mahabharat Ki (Our Story of the Mahabharat), a serialized, televised version of the ancient Indian epic Mahabharata which ran on prime-time Indian television from July to November 2008. The show was created and produced by Balaji Telefilms and Ekta Kapoor, well known throughout Asia for extremely successful prime-time soap-operas which have come to be representative of the genre in India. Kahani Hamare Mahabharat Ki was canceled quite early in its run (it was intended to air for upwards of three years) due to low ratings and intense viewer criticism of the program. The bulk of the criticism compared it unfavorably to an earlier version aired by B.R. Chopra and his team in 1988-90, which is to this day remembered as one of the most watched events in Indian television history, and is still widely seen as a largely “successful” visual translation of the story to television. This thesis analyses the dimensions of Kahani Hamare Mahabharat Ki’s promises to offer something both “old and new” to the Indian public, its internal structure, the influences upon its creation, its failure, the nature of the criticism against it, and how it sparked a large public debate about how “authenticity” and “tradition” are currently being conceptualized by modern popular media in India. The thesis takes data and evidence from a variety of scholarly, print, online, and ethnographic sources to demonstrate that Kahani Hamare Mahabharat Ki’s failure was much more complex than the case of its being simply a “bad” show; rather it reveals that to many, Chopra’s earlier version has become in some ways monolithic, containing an essential “rightness” that speaks to broader concerns about the current state of India’s cultural and religious heritage as refracted through the lens of modern media. This thesis examines Kahani Hamare Mahabharat Ki as one unique occurrence within a much broader field of mythological/devotional programming currently available in India, and points to the need for a larger scholarly study of this phenomenon.

Published
2010

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