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. |
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Postdoctoral Fellows and Research Associates
| Aftab Patel | 2021 - 2022 |
| Hadi Seyedinejad | 2016 - 2018 |
| Serge Randriambololona | 2009 - 2011 |
Graduate Students
Current
| Tian Dai | 2025 - present (Ph.D., expected 2029) |
Past
| Zack Dooley | 2023 - 2024 (M.Sc., 2024) |
| Mahan Moazzeni | 2022 - 2023 (M.Sc., 2023) |
| Aftab Patel | 2017 - 2021 (Ph.D, 2021) |
| Chandrahas Piduri | 2018 - 2019 (M.Sc., 2019) |
| 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) |
Grants Currently Held
| 2024-2029: | NSERC Individual Discovery Grant "Local Geometry of Real and Complex Analytic Mappings" |
