diff --git a/.github/workflows/build-test-pytest.yaml b/.github/workflows/build-test-pytest.yaml
index 9010f3d1a4b..bad57cee7d9 100644
--- a/.github/workflows/build-test-pytest.yaml
+++ b/.github/workflows/build-test-pytest.yaml
@@ -20,7 +20,7 @@ jobs:
         tests-type: [unit]
         include:
           - os: ubuntu-18.04
-            python-version: 3.6
+            python-version: 3.7
             dependencies: minimal
             tests-type: unit
 
diff --git a/.github/workflows/build-test.yaml b/.github/workflows/build-test.yaml
index 78dec91aab3..890cdce10fc 100644
--- a/.github/workflows/build-test.yaml
+++ b/.github/workflows/build-test.yaml
@@ -20,7 +20,7 @@ jobs:
         tests-type: [unit]
         include:
           - os: ubuntu-18.04
-            python-version: 3.6
+            python-version: 3.7
             dependencies: minimal
             tests-type: unit
           - os: ubuntu-18.04
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 3b1b5a61c5b..faa5cb8495d 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -31,7 +31,7 @@ repos:
     rev: v2.20.0
     hooks:
     - id: pyupgrade
-      args: [--py36-plus]
+      args: [--py37-plus]
 -   repo: https://github.com/psf/black
     rev: 21.6b0
     hooks:
diff --git a/conftest.py b/conftest.py
index ccdb5390739..5f1b0f05ace 100644
--- a/conftest.py
+++ b/conftest.py
@@ -6,6 +6,8 @@
 
 import pytest
 import yaml
+from matplotlib import __version__ as mpl_ver
+from packaging.version import parse as parse_version
 
 from yt.config import ytcfg
 from yt.utilities.answer_testing.testing_utilities import (
@@ -17,6 +19,9 @@
     data_dir_load,
 )
 
+MPL_VERSION = parse_version(mpl_ver)
+del mpl_ver
+
 
 def pytest_addoption(parser):
     """
@@ -109,6 +114,14 @@ def pytest_configure(config):
     ):
         config.addinivalue_line("filterwarnings", value)
 
+    if MPL_VERSION < parse_version("3.0.0"):
+        config.addinivalue_line(
+            "filterwarnings",
+            (
+                "ignore:Using or importing the ABCs from 'collections' instead of from 'collections.abc' "
+                "is deprecated since Python 3.3,and in 3.9 it will stop working:DeprecationWarning"
+            ),
+        )
     # at the time of writing, astropy's wheels are behind numpy's latest
     # version but this doesn't cause actual problems in our test suite, so
     # we allow this warning to pass.
diff --git a/pyproject.toml b/pyproject.toml
index a870568cac5..fc74bb91d16 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,19 +4,15 @@ requires = [
   # see https://github.com/numpy/numpy/pull/18389
   "wheel>=0.36.2",
 
-  # cython version is imposed by that of numpy, see release notes
-  # https://github.com/numpy/numpy/releases/tag/v1.19.2
   # Cython 3.0 is the next version after 0.29, and a major change,
   # we forbid it until we can properly test against it
-  "Cython>=0.26.1,<3.0; python_version=='3.6'",
-  "Cython>=0.29.21,<3.0; python_version>='3.7'",
+  "Cython>=0.29.21,<3.0",
   "oldest-supported-numpy",
 ]
 
 [tool.black]
 line-length = 88
 target-version = [
-  'py36',
   'py37',
   'py38',
   'py39',
diff --git a/setup.cfg b/setup.cfg
index 61ec8415497..c9a44bc6444 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -20,7 +20,6 @@ classifiers =
     Programming Language :: C
     Programming Language :: Python :: 3
     Programming Language :: Python :: 3 :: Only
-    Programming Language :: Python :: 3.6
     Programming Language :: Python :: 3.7
     Programming Language :: Python :: 3.8
     Programming Language :: Python :: 3.9
@@ -38,17 +37,16 @@ project_urls =
 packages = find:
 install_requires =
     iPython>=1.0
-    matplotlib!=3.4.2,>=2.0.2,<3.6
+    matplotlib!=3.4.2,>=2.2.3,<3.6
     more-itertools>=8.4
-    numpy>=1.13.3
+    numpy>=1.14.5
     packaging>=20.9
     pyyaml>=4.2b1
     setuptools>=19.6
-    sympy>=1.2
     toml>=0.10.2
     tqdm>=3.4.0
     unyt>=2.8.0
-python_requires = >=3.6,<3.12
+python_requires = >=3.7,<3.12
 include_package_data = True
 scripts = scripts/iyt
 zip_safe = False
@@ -93,10 +91,9 @@ mapserver =
     bottle
 minimal =
     ipython==1.0.0
-    matplotlib==2.0.2
+    matplotlib==2.2.3
     more-itertools==8.4
-    numpy==1.13.3
-    sympy==1.2
+    numpy==1.14.5
     unyt==2.8.0
 test =
     codecov~=2.0.15
diff --git a/yt/utilities/on_demand_imports.py b/yt/utilities/on_demand_imports.py
index ba519191836..862d7b161fa 100644
--- a/yt/utilities/on_demand_imports.py
+++ b/yt/utilities/on_demand_imports.py
@@ -1,7 +1,5 @@
 import sys
 
-from packaging.version import parse as parse_version
-
 
 class NotAModule:
     """
@@ -356,21 +354,6 @@ def ndimage(self):
 class h5py_imports:
     _name = "h5py"
     _err = None
-
-    def __init__(self):
-        try:
-            import h5py
-
-            if parse_version(h5py.__version__) < parse_version("2.4.0"):
-                self._err = RuntimeError(
-                    "yt requires h5py version 2.4.0 or newer, "
-                    "please update h5py with e.g. `python -m pip install -U h5py` "
-                    "and try again"
-                )
-        except ImportError:
-            pass
-        super().__init__()
-
     _File = None
 
     @property
diff --git a/yt/utilities/png_writer.py b/yt/utilities/png_writer.py
index e5314d5e932..2f36e9f453d 100644
--- a/yt/utilities/png_writer.py
+++ b/yt/utilities/png_writer.py
@@ -11,9 +11,9 @@
 
 def call_png_write_png(buffer, fileobj, dpi):
     try:
-        _png.write_png(buffer, fileobj, dpi)
-    except NameError:
         Image.fromarray(buffer).save(fileobj, dpi=(dpi, dpi), format="png")
+    except NameError:
+        _png.write_png(buffer, fileobj, dpi)
 
 
 def write_png(buffer, filename, dpi=100):
diff --git a/yt/visualization/color_maps.py b/yt/visualization/color_maps.py
index 1203e413867..210498786fc 100644
--- a/yt/visualization/color_maps.py
+++ b/yt/visualization/color_maps.py
@@ -1,12 +1,8 @@
 import numpy as np
-from matplotlib import __version__ as mpl_ver, cm as mcm, colors as cc
-from packaging.version import parse as parse_version
+from matplotlib import cm as mcm, colors as cc
 
 from . import _colormap_data as _cm
 
-MPL_VERSION = parse_version(mpl_ver)
-del mpl_ver
-
 
 def is_colormap(cmap):
     return isinstance(cmap, cc.Colormap)
@@ -260,29 +256,6 @@ def show_colormaps(subset="all", filename=None):
                 "to be 'all', 'yt_native', or a list of "
                 "valid colormap names."
             ) from e
-    if parse_version("2.0.0") <= MPL_VERSION < parse_version("2.2.0"):
-        # the reason we do this filtering is to avoid spurious warnings in CI when
-        # testing against old versions of matplotlib (currently not older than 2.0.x)
-        # and we can't easily filter warnings at the level of the relevant test itself
-        # because it's not yet run exclusively with pytest.
-        # FUTURE: remove this completely when only matplotlib 2.2+ is supported
-        deprecated_cmaps = {
-            "spectral",
-            "spectral_r",
-            "Vega10",
-            "Vega10_r",
-            "Vega20",
-            "Vega20_r",
-            "Vega20b",
-            "Vega20b_r",
-            "Vega20c",
-            "Vega20c_r",
-        }
-        for cmap in deprecated_cmaps:
-            try:
-                maps.remove(cmap)
-            except ValueError:
-                pass
 
     maps = sorted(set(maps))
     # scale the image size by the number of cmaps