Department of MathematicsWestern Science

Janusz Adamus: Research

Research Interests

Analytic geometry and local algebra: algebraic aspects of the local geometry of analytic mappings, and their effective applications to computational algebra; homological structure of modules over noetherian rings
Semialgebraic and subanalytic geometry: algebro-geometric and differential properties of subanalytic sets; analytic invariants; arc-analytic functions
Discrete mathematics: extremal graph theory, long cycles and paths; combinatorics of desingularization.
My main research interests are in the interface of real or complex analytic geometry and commutative algebra; particularly, in the study of various modes of local and global regularity of analytic and algebraic morphisms. The interplay between algebraic, topological and transcendental methods makes for one of the most beautiful and exciting mathematics. The area is well established in the classical works of Auslander, Grauert, Grothendieck, Hironaka and Remmert, to name a few. It is also at the cutting edge today due to the recent development in the effective methods of commutative algebra.
The questions about the local geometry of analytic mappings naturally involve the study of semi- and subanalytic geometry. Not only does it spin a new development in semialgebraic and subanalytic geometry, but also proves its relevance to problems in complex analysis. Most recent applications include results in singular CR geometry.

Postdoctoral Fellows

Hadi Seyedinejad 2016 - 2018
Serge Randriambololona 2009 - 2011

Graduate Students

Current

Aftab Patel 2017 - present (Ph.D., expected 2021)
Chandrahas Piduri 2018 - present (M.Sc., expected 2019)

Past

Bryan Kettle 2017 - 2018 (M.Sc., 2018)
Aftab Patel 2016 - 2017 (M.Sc., 2017)
Ashani Gamage 2015 - 2016 (M.Sc., 2016)
Nadeana Reece 2015 - 2016 (M.Sc., 2016)
John Malik 2014 - 2015 (M.Sc., 2015)
Chandrasekar Rajamani 2011 - 2012 (M.Sc., 2012)
Mahboobeh Noghrehkhaja 2009 - 2011 (M.Sc., 2011)
Hadi Seyedinejad 2009 - 2013 (Ph.D., 2013)
Enxin Wu 2007 - 2008 (M.Sc., 2008)
I am currently accepting new graduate students.
If you're considering working with me, feel free to drop a line stating your research interests and background.

Grants Currently Held

2018-2023: NSERC Individual Discovery Grant
"Local Geometry of Real and Complex Analytic Mappings"