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NishMath - #research

Matt Marshall@AI News | VentureBeat //
Microsoft is enhancing its Copilot Studio platform with AI-driven improvements, introducing deep reasoning capabilities that enable agents to tackle intricate problems through methodical thinking and combining AI flexibility with deterministic business process automation. The company has also unveiled specialized deep reasoning agents for Microsoft 365 Copilot, named Researcher and Analyst, to help users achieve tasks more efficiently. These agents are designed to function like personal data scientists, processing diverse data sources and generating insights through code execution and visualization.

Microsoft's focus includes securing AI and using it to bolster security measures, as demonstrated by the upcoming Microsoft Security Copilot agents and new security features. Microsoft aims to provide an AI-first, end-to-end security platform that helps organizations secure their future, one example being the AI agents designed to autonomously assist with phishing, data security, and identity management. The Security Copilot tool will automate routine tasks, allowing IT and security staff to focus on more complex issues, aiding in defense against cyberattacks.

Recommended read:
References :
  • Microsoft Security Blog: Learn about the upcoming availability of Microsoft Security Copilot agents and other new offerings for a more secure AI future.
  • www.zdnet.com: Designed for Microsoft's Security Copilot tool, the AI-powered agents will automate basic tasks, freeing IT and security staff to tackle more complex issues.

@sciencedaily.com //
Recent advancements in quantum computing research have yielded promising results. Researchers at the University of the Witwatersrand in Johannesburg, along with collaborators from Huzhou University in China, have discovered a method to shield quantum information from environmental disruptions, potentially leading to more reliable quantum technologies. This breakthrough involves manipulating quantum wave functions to preserve quantum information, which could enhance medical imaging, improve AI diagnostics, and strengthen data security by providing ultra-secure communication.

UK startup Phasecraft has announced a new algorithm, THRIFT, that improves the ability of quantum computers to model new materials and chemicals by a factor of 10. By optimizing quantum simulation, THRIFT enables scientists to model new materials and chemicals faster and more accurately, even on today’s slower machines. Furthermore, Oxford researchers have demonstrated a 25-nanosecond controlled-Z gate with 99.8% fidelity, combining high speed and accuracy in a simplified superconducting circuit. This achievement advances fault-tolerant quantum computing by improving raw gate performance without relying heavily on error correction or added hardware.

Recommended read:
References :
  • The Quantum Insider: Oxford Researchers Demonstrate Fast, 99.8% Fidelity Two-Qubit Gate Using Simplified Circuit Design
  • www.sciencedaily.com: Researchers find a way to shield quantum information from 'noise'

Webb Wright@Quanta Magazine //
Researchers are making significant strides in reducing the costs associated with quantum randomness, a crucial element for cryptography and simulations. Traditionally, obtaining true quantum randomness has been complex and expensive. However, the exploration of "pseudorandomness" offers a practical alternative, allowing researchers to utilize computational algorithms that mimic randomness, thus sidestepping the high costs of pure quantum randomness. This development broadens the accessibility of randomness, enabling researchers to pursue new scientific investigations.

The team from JPMorganChase, Quantinuum, multiple national labs, and UT Austin demonstrated a certified quantum randomness protocol. They showcased the first successful demonstration of a quantum computing method to generate certified randomness. Using a 56-qubit quantum machine, they output more randomness than they initially put in. What makes this truly remarkable is that this feat is considered impossible for even the most powerful classical supercomputers. This groundbreaking achievement could open new doors for quantum computing and cryptography research.

Recommended read:
References :
  • The Quantum Insider: Joint Research Team Achieves Certified Quantum Randomness, Turns Once Theoretical Experiments Into First Commercial Applications For Quantum Computing
  • Quanta Magazine: The High Cost of Quantum Randomness Is Dropping
  • hetarahulpatel.medium.com: Random Numbers Just Got Real, Thanks to Quantum Magic!

Terence Tao@What's new //
References: beuke.org , What's new
Terence Tao has recently uploaded a paper to the arXiv titled "Decomposing a factorial into large factors." The paper explores a mathematical quantity, denoted as t(N), which represents the largest value such that N! can be factorized into t(N) factors, with each factor being at least N. This concept, initially introduced by Erdös, delves into how equitably a factorial can be split into its constituent factors.

Erdös initially conjectured that an upper bound on t(N) was asymptotically sharp, implying that factorials could be split into factors of nearly uniform size for large N. However, a purported proof by Erdös, Selfridge, and Straus was lost, leading to the assertion becoming a conjecture. The paper establishes bounds on t(N), recovering a previously lost result. Further conjectures were made by Guy and Selfridge, exploring whether relationships held true for all values of N.

On March 30th, mathematical enthusiasts celebrated facts related to the number 89. Eighty-nine is a Fibonacci prime, and patterns emerge when finding it's reciprocal. Also, the number 89 can be obtained by a summation of the first 5 integers to the power of the first 5 Fibonacci numbers. 89 is also related to Armstrong numbers, which are numbers that are the sum of their digits raised to the number of digits in the number.

Recommended read:
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  • beuke.org: Your browser does not support the audio element. Profunctor optics are a modern, category-theoretic generalization of optics – bidirectional data accessors used to focus on and update parts of a data structure.
  • What's new: I;ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors“. This paper studies the quantity , defined as the largest quantity such that it is possible to factorize into factors , each of which is at least .

Tom Bridges@blogs.surrey.ac.uk //
References: blogs.surrey.ac.uk , ,
The London Mathematical Society has awarded Polina Vytnova a Research in Pairs grant, dated February 14th. The grant will enable Vytnova to host Victor Kleptsyn, a CNRS Researcher from the University of Rennes, at the University of Surrey. Together, they will collaborate on a joint research project focusing on the "Arithmetic of Cantor sets."

Also, Terry Tao has announced a collaboration with Grant Sanderson of 3blue1brown, along with Tanya Klowden, to produce a two-part video about the history of the cosmic distance ladder. This project builds upon a previous public lecture by Tao and is related to their forthcoming book. The first part of the video is already available, with Sanderson currently editing the second part.

Recommended read:
References :
  • blogs.surrey.ac.uk: Polina Vytnova has been awarded a Research in Pairs grant (Award date 14 February) by the London Mathematical Society.
  • : “Think about the knife tip. That is where you are. Now feel with it, very gently. You’re looking for a gap so small you could never see it with your eyes, but the knife tip will find it, if you put your mind there. Feel along the air till you sense the smallest little gap […]
  • What's new: Grant Sanderson (who creates the website and Youtube channel 3blue1brown) has been collaborating with myself and others (including my coauthor Tanya Klowden) on producing a two-part video giving an account of some of the history of the cosmic distance ladder, building upon a previous public lecture I gave on this topic, and also relating to […]

@phys.org //
Recent mathematical research is pushing the boundaries of theoretical understanding across various domains. One area of focus involves solving the least squares problem, particularly with rank constraints. A specific problem involves minimizing a function with a rank constraint and the quest for efficient solutions to these constrained optimization challenges remains a significant area of investigation.

This also involves a three-level exploration into a "mathematics-driven universe," questioning whether math is discovered or invented, and delving into the philosophical implications of mathematics in modern physics. Furthermore, mathematicians are employing topology to investigate the shape of the universe. This includes exploring possible 2D and 3D spaces to better understand the cosmos we inhabit, hinting at intriguing and surprising possibilities that could change our understanding of reality.

Recommended read:
References :
  • mathoverflow.net: This article focuses on solving the least square problem
  • medium.com: This article is a three-level journey into a mathematics-driven universe

@artsci.washington.edu //
University of Washington professors Xiaodong Xu, Cynthia Vinzant, and Shayan Oveis Gharan have been honored by the National Academy of Sciences (NAS) for their outstanding research achievements. The NAS awards program has been recognizing outstanding achievement in the physical, biological, and social sciences since 1866. The annual awards ceremony will honor the major contributions made by 20 researchers.

Xu received the NAS Award for Scientific Discovery for his experimental observation of the fractional quantum anomalous Hall effect. This award, presented every two years, recognizes an accomplishment or discovery in basic research within the previous five years that is expected to have a significant impact on astronomy, biochemistry, biophysics, chemistry, materials science, or physics. Xu's research explores new quantum phenomena in layered two-dimensional materials and engineered quantum systems.

Vinzant and Oveis Gharan, along with Nima Anari and Kuikui Liu, will receive the Michael and Sheila Held Prize for breakthrough work advancing the theory of matroids and mixing rates of Markov chains. The Michael and Sheila Held Prize is presented annually to honor outstanding, innovative, creative, and influential research in the areas of combinatorial and discrete optimization, or related parts of computer science, such as the design and analysis of algorithms and complexity theory. This $100,000 prize is intended to recognize recent work.

Recommended read:
References :
  • Recent News: This news article is about the NAS awards for Xu, Vinzant, and Oveis Gharan.
  • artsci.washington.edu: This page from UW describes the NAS awards for Xu, Vinzant, and Oveis Gharan.

@Department of mathematics //
References: www.ams.org , ams.org ,
The American Mathematical Society (AMS) is actively advocating for mathematics, particularly concerning the National Science Foundation (NSF). The AMS has started a page to coordinate support for professional mathematics, focusing on executive orders impacting the NSF. Recently, the NSF has seen significant changes, including the firing of 168 employees, which raises concerns about the potential impact on quantum funding and artificial intelligence research. These layoffs, occurring in response to a presidential executive order aimed at reducing the federal workforce, have affected both probationary employees and part-time experts in physics-related fields.

The AMS provides tools for the mathematical community to engage with government representatives, ensuring that the voices of mathematicians are heard in policy discussions. The AMS also actively supports mathematics on a global stage, as demonstrated by the US team earning third place at the 2025 Romanian Master of Mathematics, a challenging international high school mathematics competition, with team members earning individual awards. Penn State also rose in the NSF Higher Education Research and Development rankings. The AMS is dedicated to advancing research and connecting the diverse global mathematical community through publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.

Recommended read:
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  • www.ams.org: The American Mathematical Society has also started a page to coordinate support for professional mathematics, so far focusing on executive orders impacting the National Science Foundation:
  • ams.org: Details on NSF staff reductions, funding issues and peer-review panel postponements.
  • Terence Tao: The American Mathematical Society has also started a page to coordinate support for professional mathematics, so far focusing on executive orders impacting the National Science Foundation

Tom Bridges@blogs.surrey.ac.uk //
Recent activity in the mathematical community has highlighted the enduring fascination with mathematical constants and visual representations of mathematical concepts. A blog post on March 23, 2025, discussed a remarkably accurate approximation for pi, noting that π ≈ 3 log(640320) / √163 is exact within the limits of floating-point arithmetic, achieving accuracy to 15 decimal places. This discovery builds upon historical efforts to approximate pi, from ancient Babylonian and Egyptian calculations to Archimedes' method of exhaustion and the achievements of Chinese mathematicians like Liu Hui and Zu Chongzhi.

Visual insights in mathematics continue to be explored. A blog called Visual Insight shares striking images that help explain topics in mathematics. The creator gave a talk about it at the Illustrating Math Seminar. The blog features images created by people such as Refurio Anachro, Greg Egan, and Roice Nelson, and individual articles are available on the AMS website.

Recommended read:
References :
  • blogs.surrey.ac.uk: Details on a mathematical paper on data-driven modeling.
  • denisegaskins.com: Blog post on various mathematical topics.
  • medium.com: Refining Quantum Uncertainty Mathematics (QUM): A Structured Approach
  • medium.com: Is Mathematics a Designed System? Exploring Its Origins and Implications

@NASA //
NASA's James Webb Space Telescope (JWST) has peered into the early Universe, observing galaxies from just a few hundred million years after the Big Bang. With its unique infrared sensitivity, JWST allows researchers to examine these ancient galaxies and uncover secrets from the Universe's formative years. The telescope's NIRCam (Near-Infrared Camera) played a key role in these observations.

An international team of astronomers has identified bright hydrogen emission from a galaxy, JADES-GS-z13-1, at an unexpectedly early time. This distant galaxy, observed just 330 million years after the Big Bang, has a redshift (z) of 13, indicating its age and distance. This discovery challenges existing understanding of how light could have pierced the thick fog of neutral hydrogen that filled space at that time.

Recommended read:
References :
  • Fraser Cain: JWST was built to see the first galaxies in the Universe coming together just a few hundred million years after the Big Bang.
  • www.newscientist.com: Little red dots seen by JWST might be a kind of black hole 'star'
  • Brian Koberlein: Images of little red dots seen in several deep-sky surveys of JWST.

Tom Bridges@blogs.surrey.ac.uk //
References: Joel David Hamkins
Professor Dame Alison Etheridge from Oxford University, who is also the first President of the Academy for the Mathematical Sciences and former Chair of the REF mathematical sciences sub-panel, visited Mathematics at Surrey on March 7, 2025. She presented a colloquium talk titled "The forwards and backwards of population models," discussing a class of models suitable for modelling plant populations, which includes a novel explicit modelling of the juvenile phase and its implications for inferring data from genetics.

Tom Bridges visited the Courant Institute of Mathematical Sciences in New York on March 5, 2025, for research interaction with Yuri Latushkin. Their work focused on various research problems related to the Maslov index, Fredholm operators, and the stability of solitary waves. Additionally, Joel David Hamkins is scheduled to present a talk on modal model theory at the Panglobal Algebra and Logic Seminar at the University of Colorado Boulder on March 12, 2025, which will be available live on Zoom.

The International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2025 features a session on "Mathematical modeling applied to epidemics and the spread of bioaerosols indoors." Organized by António F. Miguel and Murat Aydin, this session highlights the importance of mathematical modeling in predicting, assessing, and controlling disease outbreaks, with a focus on indoor viral bioaerosol transmission patterns. ICNAAM aims to gather leading scientists in numerical and applied mathematics to discuss original research.

Recommended read:
References :
  • Joel David Hamkins: Introduction to modal model theory, Panglobal Algebra and Logic Seminar, Boulder, March 2025